diff --git a/cmd/mesh-host/busy_test.go b/cmd/mesh-host/busy_test.go
new file mode 100644
index 0000000..b1edaea
--- /dev/null
+++ b/cmd/mesh-host/busy_test.go
@@ -0,0 +1,66 @@
+package main
+
+import (
+	"context"
+	"sync/atomic"
+	"testing"
+	"time"
+
+	"github.com/novox/mesh-host/internal/link"
+)
+
+// A container waiting because it said busy is news when it starts waiting and when it is replaced, never on
+// its output alone (novox/hq ADR 0335): the walk waiting on this machine starts its gate at the report that
+// says it replaced, and a reconcile is otherwise silent.
+func TestABusyWaitIsSaidWhenItStartsAndWhenItEnds(t *testing.T) {
+	quiet := link.Report{Outward: []string{"eth0"}}
+	waiting := link.Report{Outward: []string{"eth0"}, Busy: []link.Busy{{ID: "build-agent.server",
+		Container: "mesh-build-agent", State: "waiting", Said: "building a"}}}
+	still := link.Report{Outward: []string{"eth0"}, Busy: []link.Busy{{ID: "build-agent.server",
+		Container: "mesh-build-agent", State: "waiting", Said: "building b, a minute on"}}}
+	replaced := link.Report{Outward: []string{"eth0"}, Busy: []link.Busy{{ID: "build-agent.server",
+		Container: "mesh-build-agent", State: "replaced-when-idle"}}}
+	if adoptionFingerprint(waiting) == adoptionFingerprint(quiet) {
+		t.Error("a container starting to wait is not news")
+	}
+	if adoptionFingerprint(still) != adoptionFingerprint(waiting) {
+		t.Error("a wait whose output changed reads as news on every ask")
+	}
+	if adoptionFingerprint(replaced) == adoptionFingerprint(waiting) {
+		t.Error("a container replaced after it waited is not news")
+	}
+	if !worthSaying(link.Report{Busy: replaced.Busy}) {
+		t.Error("a replacement after a wait is not worth saying")
+	}
+}
+
+// While a container waits, a pass is asked for every so often, not at the reconcile's five minutes; with
+// nothing waiting, none (novox/hq ADR 0335 §2).
+func TestAWaitIsAskedAgainSoonerThanTheReconcile(t *testing.T) {
+	if BusyAskEvery >= ReconcileEvery || BusyAskEvery > time.Minute {
+		t.Fatalf("a waiting container is asked every %s", BusyAskEvery)
+	}
+	var reconciles atomic.Int32
+	queue := &link.Queue{Reconcile: func(context.Context) (link.Report, bool) {
+		reconciles.Add(1)
+		return link.Report{}, false
+	}}
+	ctx, cancel := context.WithCancel(context.Background())
+	defer cancel()
+	go queue.Run(ctx)
+	busyWaiting.Store(false)
+	t.Cleanup(func() { busyWaiting.Store(false) })
+	go busyPasses(ctx, queue, 10*time.Millisecond)
+	time.Sleep(100 * time.Millisecond)
+	if n := reconciles.Load(); n != 0 {
+		t.Fatalf("%d passes were asked with nothing waiting", n)
+	}
+	busyWaiting.Store(true)
+	deadline := time.Now().Add(2 * time.Second)
+	for reconciles.Load() == 0 && time.Now().Before(deadline) {
+		time.Sleep(10 * time.Millisecond)
+	}
+	if reconciles.Load() == 0 {
+		t.Fatal("no pass was asked while a container waits")
+	}
+}
diff --git a/cmd/mesh-host/main.go b/cmd/mesh-host/main.go
index 83b5473..8c79ab3 100644
--- a/cmd/mesh-host/main.go
+++ b/cmd/mesh-host/main.go
@@ -24,6 +24,7 @@ import (
 	"sort"
 	"strings"
 	"sync"
+	"sync/atomic"
 	"syscall"
 	"text/tabwriter"
 	"time"
@@ -1259,6 +1260,7 @@ func runLink(ctx context.Context, opts options) error {
 		queue.ReconcileDue()
 	}
 	go holdTheMachine(ctx, queue)
+	go busyPasses(ctx, queue, BusyAskEvery)
 	// And whether what it runs stays up, looked at on its own clock and said when it changes (novox/hq
 	// ADR 0240) — between applies, which is when a container crash-loops.
 	if judging != nil {
@@ -1397,6 +1399,12 @@ func adoptionFingerprint(r link.Report) string {
 	// it could only speak when a declaration arrived, and a declaration cannot be composed until it
 	// has spoken: a machine waiting for a push that is waiting for the machine.
 	parts := []string{"firewall=" + r.Firewall, "outward=" + strings.Join(r.Outward, ",")}
+	// And a container waiting because it said busy, or replaced after it waited (novox/hq ADR 0335): the walk
+	// waiting on this machine starts its gate at the report that says it replaced. Not its output, which
+	// may change on every ask.
+	for _, b := range r.Busy {
+		parts = append(parts, "busy "+b.ID+"="+b.State)
+	}
 	for _, h := range r.Held {
 		parts = append(parts, "held "+h.ID+"="+h.Changed)
 	}
@@ -1736,7 +1744,7 @@ func healthAsReported(st liveness.Statement, ns *network.Statement) *link.Health
 	// LibraryContract: this engine reads a resource's declared `health` and judges it (ADR 0240 Phase B), judges a
 	// user's declared `root` (novox/hq ADR 0266), and reads a declaration's identities, groups and libraries
 	// (novox/hq ADR 0328), which is what tells the controller it may be sent any of those fields.
-	h := &link.Health{Contract: link.OwnGroupContract, At: st.At.UTC(), Resources: []link.ResourceHealth{}}
+	h := &link.Health{Contract: link.BusyContract, At: st.At.UTC(), Resources: []link.ResourceHealth{}}
 	for _, r := range st.Resources {
 		h.Resources = append(h.Resources, link.ResourceHealth{Module: r.Module, Resource: r.ID, Kind: r.Kind,
 			Target: r.Target, State: r.State, Reason: r.Reason, Since: r.Since.UTC(), Streak: r.Streak,
@@ -1868,6 +1876,32 @@ func holdTheMachine(ctx context.Context, queue *link.Queue) {
 	}
 }
 
+// busyWaiting is whether the last apply left a container running because it said busy (novox/hq ADR 0335).
+var busyWaiting atomic.Bool
+
+// BusyAskEvery is how often a container waiting because it said busy is asked again (novox/hq ADR 0335 §2):
+// each ask is a pass of its own, so a build that ends is followed by its replacement within this, not
+// within the reconcile's five minutes — and the bound of 15 minutes is met within this of its end.
+const BusyAskEvery = 20 * time.Second
+
+// busyPasses asks for a pass every so often while a container waits because it said busy. **It asks; it
+// does not apply**, as holdTheMachine: the queue's worker does, when its turn comes, so a pass never holds
+// the machine for the wait, and a delivery waiting is that pass's apply.
+func busyPasses(ctx context.Context, queue *link.Queue, every time.Duration) {
+	ticker := time.NewTicker(every)
+	defer ticker.Stop()
+	for {
+		select {
+		case <-ctx.Done():
+			return
+		case <-ticker.C:
+			if busyWaiting.Load() {
+				queue.ReconcileDue()
+			}
+		}
+	}
+}
+
 // reconcileKept is the reconcile's act, as the queue's worker runs it: hold the machine to what it
 // was last told, read once it is this act's turn, and say what did not go.
 //
@@ -1919,7 +1953,7 @@ func worthSaying(report link.Report) bool {
 	}
 	return len(report.Held) > 0 || report.Firewall != "" || len(report.Outward) > 0 ||
 		len(report.Filters) > 0 || report.FoundFirewall != nil || len(report.Windows) > 0 ||
-		len(report.Rollbacks) > 0
+		len(report.Rollbacks) > 0 || len(report.Busy) > 0
 }
 
 // announceOr is what the apply writes its detail with, given what the caller has to say things with.
@@ -2168,6 +2202,14 @@ func applyAndKeepHeld(ctx context.Context, opts options, raw []byte, signed *sto
 	for _, w := range outcome.Windows {
 		report.Windows = append(report.Windows, link.Window{Step: w.Step, Holds: w.Holds, Since: w.Opened, Until: w.Until})
 	}
+	// And a container left running because it said busy, or replaced after it waited (novox/hq ADR 0335):
+	// the walk waiting on this machine reads it. While one waits, this machine asks it again sooner than its
+	// reconcile (busyPasses).
+	for _, b := range outcome.Busy {
+		report.Busy = append(report.Busy, link.Busy{ID: b.ID, Container: b.Container, State: b.State,
+			Since: b.Since, Until: b.Until, Said: b.Said})
+	}
+	busyWaiting.Store(outcome.Waiting())
 	// And what runs here that nobody asked for (novox/hq ADR 0163).
 	if strays, err := apply.Strays(ctx, apply.ExecRunner, updated); err != nil {
 		fmt.Fprintf(os.Stderr, "mesh-host: applied, and could not list what else runs here: %v\n", err)
diff --git a/cmd/mesh-host/units_test.go b/cmd/mesh-host/units_test.go
index 0084497..61e98a0 100644
--- a/cmd/mesh-host/units_test.go
+++ b/cmd/mesh-host/units_test.go
@@ -87,10 +87,10 @@ func TestTheStatementSaysAnAccountJudgedForRoot(t *testing.T) {
 			Groups: []string{"openrazer"}}, State: accounts.Healthy, Since: at},
 	}}
 	h := withAccounts(healthAsReported(liveness.Statement{At: at}, nil), as)
-	// At RootContract or later: an engine that also reads an identity's runner says OwnGroupContract (novox/hq ADR
-	// 0334), one above ADR 0328's LibraryContract.
-	if h.Contract < link.RootContract || link.RootContract != 3 || h.Contract != link.OwnGroupContract ||
-		link.OwnGroupContract != link.LibraryContract+1 {
+	// At RootContract or later: an engine that also reads a container's busy says BusyContract (novox/hq ADR
+	// 0335), one above ADR 0334's OwnGroupContract.
+	if h.Contract < link.RootContract || link.RootContract != 3 || h.Contract != link.BusyContract ||
+		link.BusyContract != link.OwnGroupContract+1 {
 		t.Fatalf("contract %d", h.Contract)
 	}
 	got := map[string]string{}
diff --git a/internal/apply/apply.go b/internal/apply/apply.go
index dbad871..3695a09 100644
--- a/internal/apply/apply.go
+++ b/internal/apply/apply.go
@@ -92,6 +92,11 @@ type Outcome struct {
 	// reads is, for a container, the digest of each file it was created reading, by path — so
 	// the next apply can say which one changed (novox/hq 04-ISSUES/103).
 	reads map[string]string
+	// busySince is, for a container left running because it said busy, when the first apply that would
+	// have replaced it ran (novox/hq ADR 0335): kept in its record, so the bound holds across passes and
+	// across a restart of the node-engine. busy is what the report says of it.
+	busySince *time.Time
+	busy      *BusyWait
 }
 
 // Report is what an apply did, in the order it did it.
@@ -108,6 +113,20 @@ type Report struct {
 	// 224): a machine whose server is stopped at 03:31 because its collector is running is
 	// working, not broken, and the report is where that difference is said.
 	Windows []Window `json:"windows,omitempty"`
+	// Busy is every container this apply left running because it said busy, or replaced after it had
+	// waited (novox/hq ADR 0335): a machine whose walk waits for it says why, and how it ended.
+	Busy []BusyWait `json:"busy,omitempty"`
+}
+
+// Waiting says whether a container of this apply waits to be replaced because it is busy: what makes the
+// node-engine ask again sooner than its reconcile (novox/hq ADR 0335 §2).
+func (r Report) Waiting() bool {
+	for _, b := range r.Busy {
+		if b.State == BusyWaiting {
+			return true
+		}
+	}
+	return false
 }
 
 // Changed reports whether anything about the machine actually moved. An apply that changed
@@ -118,7 +137,10 @@ func (r Report) Changed() bool {
 		// whose account's manager is not running, which nothing moved either (novox/hq ADR 0177);
 		// held still is a container a maintenance window stopped, which the apply did not touch
 		// (novox/hq issue 224).
-		if o.Action != "unchanged" && o.Action != "held" && o.Action != "waiting" && o.Action != heldStill {
+		// waits busy is a container left running because it said busy (novox/hq ADR 0335), which nothing
+		// moved either.
+		if o.Action != "unchanged" && o.Action != "held" && o.Action != "waiting" && o.Action != heldStill &&
+			o.Action != waitsBusy {
 			return true
 		}
 	}
@@ -987,6 +1009,7 @@ func ApplyMindingWindows(
 			KeptMode:     keptMode,
 			KeptOwner:    keptOwner,
 			Reads:        outcome.reads,
+			BusySince:    outcome.busySince,
 			Stateless:    outcome.stateless,
 			Scope:        outcome.scope,
 			User:         outcome.user,
@@ -1046,7 +1069,10 @@ func ApplyMindingWindows(
 				Action: "forgotten", Detail: detail})
 			log(fmt.Sprintf("  forgotten %s (%s): %s", from.ID, from.Target, detail))
 		}
-		if outcome.Action == heldStill {
+		if outcome.busy != nil {
+			report.Busy = append(report.Busy, *outcome.busy)
+		}
+		if outcome.Action == heldStill || outcome.Action == waitsBusy {
 			// Not changed: nothing about it moved, so nothing that restarts on it restarts.
 			log(fmt.Sprintf("  %s %s (%s): %s", outcome.Action, outcome.ID, outcome.Target, outcome.Detail))
 		} else if outcome.Action != "unchanged" {
@@ -2707,6 +2733,15 @@ func applyContainer(ctx context.Context, r *declaration.Container, run Runner,
 		out.Action = "unchanged"
 		return out, nil
 	case existed:
+		// **A container that says it is busy is asked before it is replaced** (novox/hq ADR 0335 §2): left
+		// running while it says busy, within the bound, and replaced on the first pass it says idle. Only a
+		// running one: a stopped container holds no work in hand.
+		if r.Busy != nil && before.Running {
+			if waits := askBeforeReplacing(ctx, r, run, cri, previous, &out); waits {
+				out.reads = wasReading
+				return out, nil
+			}
+		}
 		if _, err := run(ctx, cri, "rm", "-f", r.Name); err != nil {
 			return out, fmt.Errorf("replacing container %s: %w", r.Name, err)
 		}
@@ -2807,6 +2842,9 @@ func applyContainer(ctx context.Context, r *declaration.Container, run Runner,
 		default:
 			out.Detail = "replaced; a container's configuration is fixed when it is created"
 		}
+		if out.busy != nil {
+			out.Detail += "; " + out.busy.Words()
+		}
 	}
 	return out, nil
 }
diff --git a/internal/apply/busy.go b/internal/apply/busy.go
new file mode 100644
index 0000000..0c80bfb
--- /dev/null
+++ b/internal/apply/busy.go
@@ -0,0 +1,139 @@
+package apply
+
+import (
+	"context"
+	"fmt"
+	"strings"
+	"time"
+	"unicode/utf8"
+
+	"github.com/novox/mesh-host/internal/declaration"
+	"github.com/novox/mesh-host/internal/store"
+)
+
+// A container that says it is busy is replaced once it is idle, within a bound (novox/hq ADR 0335).
+//
+// **Asked, never waited on.** The apply asks the container once, and while it says busy leaves it running
+// as it is and goes on with everything else of the declaration: the machine's lock is held for one ask,
+// never for the wait. The wait is carried between passes in the container's record (store.Applied's
+// BusySince), so the next pass — the node-engine asks again sooner than its reconcile while anything waits
+// — asks again, and so does a node-engine started again in between: the bound runs from the first apply
+// that would have replaced the container, whoever applied it.
+
+// waitsBusy is the action of a container left running because it said busy (novox/hq ADR 0335 §2). Its own
+// word rather than "unchanged": its declaration moved, and the machine is not yet what was declared.
+const waitsBusy = "waits-busy"
+
+// What a report says of a busy container (novox/hq ADR 0335 §2, §3).
+const (
+	// BusyWaiting is a container left running because it said busy, waiting to be replaced.
+	BusyWaiting = "waiting"
+	// BusyReplacedIdle is a container replaced on the first pass it said idle, after it had waited.
+	BusyReplacedIdle = "replaced-when-idle"
+	// BusyReplacedAtBound is a container still busy at the bound, replaced anyway.
+	BusyReplacedAtBound = "replaced-at-bound"
+)
+
+// BusyWait is one container a busy command held, as a report says it.
+type BusyWait struct {
+	// ID is the resource's id (`<module>.<resource>`), Container its runtime name.
+	ID        string `json:"id"`
+	Container string `json:"container"`
+	// State is BusyWaiting, BusyReplacedIdle or BusyReplacedAtBound.
+	State string `json:"state"`
+	// Since is when the first apply that would have replaced it ran; Until when the bound replaces it.
+	Since time.Time `json:"since"`
+	Until time.Time `json:"until"`
+	// Said is the last output its busy command gave.
+	Said string `json:"said,omitempty"`
+}
+
+// Words is the wait in a sentence, for an outcome's detail and the console.
+func (b BusyWait) Words() string {
+	since := b.Since.UTC().Format(time.RFC3339)
+	said := ""
+	if b.Said != "" {
+		said = "; its busy command last said: " + b.Said
+	}
+	switch b.State {
+	case BusyReplacedAtBound:
+		return fmt.Sprintf("replaced while still busy: it said busy since %s and the bound of %s ran out "+
+			"(novox/hq ADR 0335 §3)%s", since, declaration.BusyBound, said)
+	case BusyReplacedIdle:
+		return fmt.Sprintf("replaced once it said idle, after waiting since %s (novox/hq ADR 0335 §2)%s", since, said)
+	}
+	return fmt.Sprintf("busy: left running and replaced on the first pass it says idle, or at %s at the latest; "+
+		"waiting since %s (novox/hq ADR 0335 §2)%s", b.Until.UTC().Format(time.RFC3339), since, said)
+}
+
+// busyClock is the clock the bound is read on. A test moves it.
+var busyClock = time.Now
+
+// busySaidMost is how much of a busy command's output a report carries: its last lines, enough to say what
+// it held.
+const busySaidMost = 400
+
+// askBeforeReplacing asks a running container that declares busy whether it may be replaced now, and says
+// in out what came of it. True when it waits: out is then the whole outcome of this pass. False when the
+// caller replaces it — idle, or past the bound — with out carrying the wait it ended, if there was one.
+func askBeforeReplacing(ctx context.Context, r *declaration.Container, run Runner, cri string,
+	previous store.Applied, out *Outcome) bool {
+	now := busyClock().UTC()
+	busy, said := askBusy(ctx, r, run, cri)
+	var since time.Time
+	waited := previous.BusySince != nil && previous.Target == r.Name
+	if waited {
+		since = previous.BusySince.UTC()
+	}
+	wait := BusyWait{ID: r.ID, Container: r.Name, Since: since, Said: said}
+	switch {
+	case !busy && !waited:
+		// Idle at the first ask: replaced at once, as a container that declares nothing is.
+		return false
+	case !busy:
+		wait.State, wait.Until = BusyReplacedIdle, since.Add(declaration.BusyBound)
+		out.busy = &wait
+		return false
+	}
+	if !waited {
+		since = now
+		wait.Since = now
+	}
+	wait.Until = since.Add(declaration.BusyBound)
+	if !now.Before(wait.Until) {
+		wait.State = BusyReplacedAtBound
+		out.busy = &wait
+		return false
+	}
+	wait.State = BusyWaiting
+	out.Action, out.Detail = waitsBusy, wait.Words()
+	out.busySince, out.busy = &since, &wait
+	return true
+}
+
+// askBusy runs a container's busy command inside it, by its shell, as an exec health check is run: busy is
+// an exit of 0 and nothing else. An ask that could not be made, or did not answer within its timeout, is
+// not busy: the bound is what keeps a container whose command never answers from being held.
+func askBusy(ctx context.Context, r *declaration.Container, run Runner, cri string) (bool, string) {
+	ask, cancel := context.WithTimeout(ctx, r.Busy.Within())
+	defer cancel()
+	output, err := run(ask, cri, "exec", r.Name, "/bin/sh", "-c", r.Busy.Command)
+	said := strings.TrimSpace(output)
+	if err != nil && said == "" {
+		said = err.Error()
+	}
+	return err == nil, lastOf(said, busySaidMost)
+}
+
+// lastOf is the end of a text, at most n bytes, on one line.
+func lastOf(s string, n int) string {
+	s = strings.Join(strings.Fields(s), " ")
+	if len(s) <= n {
+		return s
+	}
+	from := len(s) - n
+	for from < len(s) && !utf8.RuneStart(s[from]) {
+		from++
+	}
+	return "…" + s[from:]
+}
diff --git a/internal/apply/busy_test.go b/internal/apply/busy_test.go
new file mode 100644
index 0000000..5f5c25d
--- /dev/null
+++ b/internal/apply/busy_test.go
@@ -0,0 +1,326 @@
+package apply
+
+import (
+	"context"
+	"errors"
+	"path/filepath"
+	"slices"
+	"strings"
+	"sync"
+	"testing"
+	"time"
+
+	"github.com/novox/mesh-host/internal/declaration"
+	"github.com/novox/mesh-host/internal/store"
+)
+
+// A container that says it is busy is replaced once it is idle, within a bound (novox/hq ADR 0335). The
+// machine of these tests runs two containers, a build agent that declares `busy` and a web server that
+// does not; every call that replaces a container is counted.
+
+type aBusyMachine struct {
+	mu sync.Mutex
+	// containers is each container's name and the spec it was created with; running whether it runs.
+	containers map[string]string
+	busy       bool   // what the agent's busy command answers
+	said       string // what it prints
+	asked      int
+	calls      []string
+}
+
+func newBusyMachine() *aBusyMachine {
+	return &aBusyMachine{containers: map[string]string{}}
+}
+
+func (m *aBusyMachine) run(_ context.Context, _ string, args ...string) (string, error) {
+	m.mu.Lock()
+	defer m.mu.Unlock()
+	switch args[0] {
+	case "info", "image":
+		return "27.0\n", nil
+	case "container": // inspect
+		name := args[len(args)-1]
+		spec, there := m.containers[name]
+		if !there {
+			return "", errors.New("no such container")
+		}
+		return "true\t" + spec, nil
+	case "exec":
+		m.asked++
+		m.calls = append(m.calls, "ask "+args[1])
+		if strings.Join(args[2:], " ") != "/bin/sh -c mesh-builder busy" {
+			return "", errors.New("asked something else: " + strings.Join(args[2:], " "))
+		}
+		if m.busy {
+			return m.said + "\n", nil
+		}
+		return m.said + "\n", errors.New("exited 1")
+	case "rm":
+		name := args[len(args)-1]
+		m.calls = append(m.calls, "rm "+name)
+		delete(m.containers, name)
+	case "run":
+		name := args[slices.Index(args, "--name")+1]
+		m.calls = append(m.calls, "create "+name)
+		for i, a := range args {
+			if a == "--label" && strings.HasPrefix(args[i+1], specLabel+"=") {
+				m.containers[name] = strings.TrimPrefix(args[i+1], specLabel+"=")
+			}
+		}
+	}
+	return "", nil
+}
+
+func (m *aBusyMachine) mark() int {
+	m.mu.Lock()
+	defer m.mu.Unlock()
+	return len(m.calls)
+}
+
+// since is every call since mark that replaced a container, or asked one.
+func (m *aBusyMachine) since(mark int) []string {
+	m.mu.Lock()
+	defer m.mu.Unlock()
+	return append([]string(nil), m.calls[mark:]...)
+}
+
+func (m *aBusyMachine) answer(busy bool, said string) {
+	m.mu.Lock()
+	defer m.mu.Unlock()
+	m.busy, m.said = busy, said
+}
+
+// twoContainers is the declaration at a version: v moves the agent's image tag through its env, w the web's.
+func twoContainers(t *testing.T, agent, web string) *declaration.Declaration {
+	t.Helper()
+	return parse(t, `{"declaration":1,"resources":[
+	  {"id":"build-agent.server","type":"container","name":"mesh-build-agent","image":"`+pinned+`",
+	   "env":{"V":"`+agent+`"},"busy":{"command":"mesh-builder busy","timeout":"5s"}},
+	  {"id":"web.server","type":"container","name":"web","image":"`+pinned+`","env":{"V":"`+web+`"}}
+	]}`)
+}
+
+// atClock moves the bound's clock for one test.
+func atClock(t *testing.T, at *time.Time) {
+	t.Helper()
+	was := busyClock
+	busyClock = func() time.Time { return *at }
+	t.Cleanup(func() { busyClock = was })
+}
+
+func busyOf(r Report, id string) (BusyWait, bool) {
+	for _, b := range r.Busy {
+		if b.ID == id {
+			return b, true
+		}
+	}
+	return BusyWait{}, false
+}
+
+func applyBusy(t *testing.T, m *aBusyMachine, d *declaration.Declaration, known store.State) (Report, store.State) {
+	t.Helper()
+	report, state, err := Apply(context.Background(), archHost(t), d, known, store.OriginDeclared, m.run, nil, nil)
+	if err != nil {
+		t.Fatalf("the apply failed: %v", err)
+	}
+	return report, state
+}
+
+// The decision's first check: an apply that would replace a container whose busy command exits 0 leaves it
+// running, applies the rest, and replaces it on the first pass the command exits non-zero.
+func TestABusyContainerIsLeftRunningAndReplacedOnTheFirstPassItSaysIdle(t *testing.T) {
+	now := time.Date(2026, 10, 13, 1, 0, 0, 0, time.UTC)
+	atClock(t, &now)
+	m := newBusyMachine()
+	_, state := applyBusy(t, m, twoContainers(t, "1", "1"), store.State{})
+
+	// A merge moves both: the agent holds a build, the web server holds nothing.
+	m.answer(true, "building novox/mesh-controller (check of #280) since 00:58")
+	mark := m.mark()
+	report, state := applyBusy(t, m, twoContainers(t, "2", "2"), state)
+	if got := m.since(mark); !slices.Equal(got, []string{"ask mesh-build-agent", "rm web", "create web"}) {
+		t.Fatalf("a busy agent was not left running while the rest applied: %v", got)
+	}
+	o := outcomeOf(report, "build-agent.server")
+	if o.Action != waitsBusy {
+		t.Fatalf("a busy container was reported %q, want %q: %+v", o.Action, waitsBusy, o)
+	}
+	for _, says := range []string{"busy", "first pass it says idle", "check of #280", "ADR 0335"} {
+		if !strings.Contains(o.Detail, says) {
+			t.Errorf("the outcome does not say %q: %s", says, o.Detail)
+		}
+	}
+	if (Report{Outcomes: []Outcome{o}}).Changed() {
+		t.Errorf("a container left running reads as a change: %+v", o)
+	}
+	b, said := busyOf(report, "build-agent.server")
+	if !said || b.State != BusyWaiting || !b.Since.Equal(now) || !b.Until.Equal(now.Add(15*time.Minute)) ||
+		b.Container != "mesh-build-agent" || !strings.Contains(b.Said, "check of #280") {
+		t.Fatalf("the report does not say the agent waits, since when and until when: %+v", report.Busy)
+	}
+	if !report.Waiting() {
+		t.Error("a report with a container waiting does not say so")
+	}
+	if rec, _ := state.Find("build-agent.server"); rec.BusySince == nil || !rec.BusySince.Equal(now) {
+		t.Fatalf("the wait is not kept in the container's record: %+v", rec)
+	}
+
+	// Asked again a minute later, still busy: still left running, the wait counted from the first apply.
+	now = now.Add(time.Minute)
+	mark = m.mark()
+	report, state = applyBusy(t, m, twoContainers(t, "2", "2"), state)
+	if got := m.since(mark); !slices.Equal(got, []string{"ask mesh-build-agent"}) {
+		t.Fatalf("a second pass while busy did more than ask: %v", got)
+	}
+	if b, _ := busyOf(report, "build-agent.server"); b.State != BusyWaiting || !b.Since.Equal(now.Add(-time.Minute)) {
+		t.Fatalf("the second pass does not keep the wait from the first apply: %+v", report.Busy)
+	}
+
+	// The build ends: the next pass replaces it, and says it waited.
+	now = now.Add(time.Minute)
+	m.answer(false, "idle")
+	mark = m.mark()
+	report, state = applyBusy(t, m, twoContainers(t, "2", "2"), state)
+	if got := m.since(mark); !slices.Equal(got, []string{"ask mesh-build-agent", "rm mesh-build-agent", "create mesh-build-agent"}) {
+		t.Fatalf("the agent was not replaced on the first pass it said idle: %v", got)
+	}
+	if o := outcomeOf(report, "build-agent.server"); o.Action != "updated" || !strings.Contains(o.Detail, "once it said idle") {
+		t.Errorf("the replacement does not say it waited: %+v", o)
+	}
+	if b, _ := busyOf(report, "build-agent.server"); b.State != BusyReplacedIdle {
+		t.Errorf("the report does not say the agent was replaced when idle: %+v", report.Busy)
+	}
+	if report.Waiting() {
+		t.Error("a report with nothing waiting says something waits")
+	}
+	if rec, _ := state.Find("build-agent.server"); rec.BusySince != nil {
+		t.Errorf("the wait is still kept after the replacement: %+v", rec)
+	}
+
+	// And the pass after that has nothing to say about it.
+	report, _ = applyBusy(t, m, twoContainers(t, "2", "2"), state)
+	if len(report.Busy) != 0 {
+		t.Errorf("a container replaced is still said: %+v", report.Busy)
+	}
+}
+
+// An idle container is replaced at once, as one that declares nothing is: asked once, nothing waits.
+func TestAnIdleContainerIsReplacedAtOnce(t *testing.T) {
+	m := newBusyMachine()
+	_, state := applyBusy(t, m, twoContainers(t, "1", "1"), store.State{})
+	m.answer(false, "")
+	mark := m.mark()
+	report, _ := applyBusy(t, m, twoContainers(t, "2", "1"), state)
+	if got := m.since(mark); !slices.Equal(got, []string{"ask mesh-build-agent", "rm mesh-build-agent", "create mesh-build-agent"}) {
+		t.Fatalf("an idle agent was not replaced at once: %v", got)
+	}
+	if len(report.Busy) != 0 {
+		t.Errorf("an idle container replaced at once is said as a wait: %+v", report.Busy)
+	}
+	// And a container whose declaration did not move is never asked.
+	mark = m.mark()
+	applyBusy(t, m, twoContainers(t, "2", "1"), state)
+	if got := m.since(mark); slices.Contains(got, "ask mesh-build-agent") {
+		t.Errorf("a container nothing replaces was asked: %v", got)
+	}
+}
+
+// Past the bound it is replaced anyway, the report carrying the command's last output — and the bound holds
+// across a restart of the node-engine: the wait is read back from the state on disk.
+func TestABusyContainerIsReplacedAtTheBoundEvenAfterARestart(t *testing.T) {
+	now := time.Date(2026, 10, 13, 1, 0, 0, 0, time.UTC)
+	atClock(t, &now)
+	m := newBusyMachine()
+	_, state := applyBusy(t, m, twoContainers(t, "1", "1"), store.State{})
+	m.answer(true, "building novox/mesh-host (a check that never ends)")
+	_, state = applyBusy(t, m, twoContainers(t, "2", "1"), state)
+
+	// The node-engine stops and starts again: what it knows is what it saved.
+	path := filepath.Join(t.TempDir(), "state.json")
+	if err := store.Save(path, state); err != nil {
+		t.Fatal(err)
+	}
+	reloaded, err := store.Load(path)
+	if err != nil {
+		t.Fatal(err)
+	}
+
+	now = now.Add(14 * time.Minute)
+	mark := m.mark()
+	report, reloaded := applyBusy(t, m, twoContainers(t, "2", "1"), reloaded)
+	if got := m.since(mark); slices.Contains(got, "rm mesh-build-agent") {
+		t.Fatalf("a container busy within the bound was replaced after a restart: %v", got)
+	}
+	if b, _ := busyOf(report, "build-agent.server"); b.State != BusyWaiting || !b.Since.Equal(now.Add(-14*time.Minute)) {
+		t.Fatalf("a restart started the wait again: %+v", report.Busy)
+	}
+
+	now = now.Add(time.Minute)
+	mark = m.mark()
+	report, _ = applyBusy(t, m, twoContainers(t, "2", "1"), reloaded)
+	if got := m.since(mark); !slices.Equal(got, []string{"ask mesh-build-agent", "rm mesh-build-agent", "create mesh-build-agent"}) {
+		t.Fatalf("a container still busy at the bound was not replaced: %v", got)
+	}
+	b, _ := busyOf(report, "build-agent.server")
+	if b.State != BusyReplacedAtBound || !strings.Contains(b.Said, "never ends") {
+		t.Fatalf("the report does not say it replaced a busy container, with its last output: %+v", report.Busy)
+	}
+	if o := outcomeOf(report, "build-agent.server"); !strings.Contains(o.Detail, "still busy") ||
+		!strings.Contains(o.Detail, "never ends") {
+		t.Errorf("the outcome does not say a busy container was replaced, with what it said: %s", o.Detail)
+	}
+}
+
+// While one container waits, a send that changes another module on the same machine is applied at once: the
+// apply returns after one ask, and holds nothing for the wait.
+func TestASendToAnotherModuleIsAppliedWhileOneWaits(t *testing.T) {
+	now := time.Date(2026, 10, 13, 1, 0, 0, 0, time.UTC)
+	atClock(t, &now)
+	m := newBusyMachine()
+	_, state := applyBusy(t, m, twoContainers(t, "1", "1"), store.State{})
+	m.answer(true, "building")
+	_, state = applyBusy(t, m, twoContainers(t, "2", "1"), state)
+
+	// The next send moves only the web server.
+	mark := m.mark()
+	done := make(chan struct{})
+	var report Report
+	go func() {
+		defer close(done)
+		report, _ = applyBusy(t, m, twoContainers(t, "2", "2"), state)
+	}()
+	select {
+	case <-done:
+	case <-time.After(5 * time.Second):
+		t.Fatal("an apply while a container waits did not return")
+	}
+	got := m.since(mark)
+	if !slices.Contains(got, "create web") || slices.Contains(got, "rm mesh-build-agent") {
+		t.Fatalf("the other module's send was not applied at once beside the wait: %v", got)
+	}
+	if o := outcomeOf(report, "web.server"); o.Action != "updated" {
+		t.Errorf("the web server was reported %q: %+v", o.Action, o)
+	}
+}
+
+// A container's busy is held to its shape where it arrives.
+func TestBusyIsReadAndHeldToItsShape(t *testing.T) {
+	d := twoContainers(t, "1", "1")
+	c := d.Resources[0].(*declaration.Container)
+	if c.Busy == nil || c.Busy.Command != "mesh-builder busy" || c.Busy.Within() != 5*time.Second {
+		t.Fatalf("busy was not read: %+v", c.Busy)
+	}
+	for name, raw := range map[string]string{
+		"no command":     `"busy":{"command":" "}`,
+		"a long timeout": `"busy":{"command":"x","timeout":"5m"}`,
+		"not a duration": `"busy":{"command":"x","timeout":"soon"}`,
+		"an unknown key": `"busy":{"command":"x","every":"1m"}`,
+		"on a step":      `"run-once":true,"busy":{"command":"x"}`,
+	} {
+		_, err := declaration.Parse([]byte(`{"declaration":1,"resources":[{"id":"a.b","type":"container",` +
+			`"name":"b","image":"` + pinned + `",` + raw + `}]}`))
+		if err == nil {
+			t.Errorf("%s: a busy of that shape was accepted", name)
+		}
+	}
+}
diff --git a/internal/declaration/busy.go b/internal/declaration/busy.go
new file mode 100644
index 0000000..3b73485
--- /dev/null
+++ b/internal/declaration/busy.go
@@ -0,0 +1,87 @@
+package declaration
+
+import (
+	"bytes"
+	"encoding/json"
+	"fmt"
+	"strings"
+	"time"
+)
+
+// Busy is how a long-running container says it holds work that would be lost if it were stopped now
+// (novox/hq ADR 0335 §1): a command run inside it, by its shell, as an exec health check is, that exits 0
+// while it is busy and non-zero when it is idle. Being asked is also the container's notice that it is
+// about to be replaced: from the first ask it takes no new work, so its answer ends once the work in hand
+// ends.
+//
+// **Not part of what the container is.** Busy is not in the container's spec: a changed command changes
+// when the container is replaced, never whether — a container is not recreated for its busy command alone.
+type Busy struct {
+	Command string `json:"command"`
+	// Timeout is how long one ask may take; empty is BusyTimeoutDefault.
+	Timeout string `json:"timeout,omitempty"`
+}
+
+// The bounds of an ask (novox/hq ADR 0335).
+const (
+	BusyTimeoutDefault = 10 * time.Second
+	// BusyTimeoutCeiling is the longest one ask may take: an ask runs inside an apply, and an apply waits
+	// for nothing longer than a look.
+	BusyTimeoutCeiling = time.Minute
+	// BusyBound is how long a container that says busy is left running after the first apply that would
+	// have replaced it (ADR 0335 §3). The node-engine's, not the module's: no module holds its own
+	// replacement for ever.
+	BusyBound = 15 * time.Minute
+)
+
+// UnmarshalJSON reads a busy strictly, as everything a declaration carries is read.
+func (b *Busy) UnmarshalJSON(raw []byte) error {
+	type plain Busy
+	var p plain
+	dec := json.NewDecoder(bytes.NewReader(raw))
+	dec.DisallowUnknownFields()
+	if err := dec.Decode(&p); err != nil {
+		return fmt.Errorf("busy: %w", err)
+	}
+	*b = Busy(p)
+	return nil
+}
+
+// Within is how long one ask may take. Validated on arrival, so an unreadable timeout is the default.
+func (b *Busy) Within() time.Duration {
+	if d, err := time.ParseDuration(b.Timeout); err == nil && d > 0 {
+		return d
+	}
+	return BusyTimeoutDefault
+}
+
+// problems holds a container's busy to its shape: a one-line command, a timeout within its bounds, and only
+// on a container that stays up.
+func (b *Busy) problems(where string, longRunning bool) []string {
+	if b == nil {
+		return nil
+	}
+	var problems []string
+	say := func(format string, args ...any) {
+		problems = append(problems, where+": "+fmt.Sprintf(format, args...))
+	}
+	if !longRunning {
+		say("busy is asked of a container that stays up; a step or a scheduled run is never replaced mid-run")
+	}
+	if strings.TrimSpace(b.Command) == "" {
+		say("busy needs a command")
+	}
+	if strings.ContainsAny(b.Command, "\n\r") {
+		say("busy's command is one line")
+	}
+	if b.Timeout != "" {
+		d, err := time.ParseDuration(b.Timeout)
+		switch {
+		case err != nil:
+			say("busy's timeout is a duration, not %q", b.Timeout)
+		case d <= 0 || d > BusyTimeoutCeiling:
+			say("an ask of busy takes more than nothing and at most %s, not %s", BusyTimeoutCeiling, d)
+		}
+	}
+	return problems
+}
diff --git a/internal/declaration/declaration.go b/internal/declaration/declaration.go
index 4e54fc7..a265afa 100644
--- a/internal/declaration/declaration.go
+++ b/internal/declaration/declaration.go
@@ -1239,6 +1239,11 @@ type Container struct {
 	// timing, judged by the node-engine beside liveness. Absent: judged alive or not, and nothing more.
 	Health *Health `json:"health,omitempty"`
 
+	// Busy is how this container says it holds work a replacement would lose (novox/hq ADR 0335): asked
+	// before it is replaced, and while it says busy it is left running, within the bound. Absent: never
+	// busy, and replaced at once, as before.
+	Busy *Busy `json:"busy,omitempty"`
+
 	// RunAs is who the container runs as, resolved by the controller from the module's identity and the
 	// image's declared interface (novox/hq ADR 0325 §2, §3): told by environment (the image reads PUID and
 	// PGID, say) or by the runtime's own user option. Part of the spec, so a change recreates it. Absent: the
@@ -1318,6 +1323,7 @@ func (c *Container) Target() string   { return c.Name }
 
 func (c *Container) validate(where string, _ bool) []string {
 	problems := c.Health.problems(where, true, !c.RunOnce && c.Schedule == "")
+	problems = append(problems, c.Busy.problems(where, !c.RunOnce && c.Schedule == "")...)
 	if c.Name == "" {
 		problems = append(problems, where+": a container needs a name")
 	}
diff --git a/internal/link/messages.go b/internal/link/messages.go
index 08b237c..0dc192e 100644
--- a/internal/link/messages.go
+++ b/internal/link/messages.go
@@ -174,6 +174,14 @@ type Report struct {
 	// broken.
 	Windows []Window `json:"windows,omitempty"`
 
+	// Busy is every container the apply that reports left running because it said busy, and every one it
+	// replaced after it had waited, with how (novox/hq ADR 0335): `waiting`, `replaced-when-idle` or
+	// `replaced-at-bound`, since when, until when at the latest, and the last output of its busy command.
+	// A walk waiting on this machine for a module whose container is listed `waiting` waits for the report
+	// that no longer lists it so: its first-machine gate starts then (ADR 0335 §4). Absent from an engine
+	// older than BusyContract, which never waits.
+	Busy []Busy `json:"busy,omitempty"`
+
 	// Strays is what runs on the machine that the mesh neither wrote nor holds (novox/hq ADR
 	// 0163): containers nobody declared and nobody holds, the ones a cutover leaves behind.
 	Strays []Stray `json:"strays,omitempty"`
@@ -280,6 +288,13 @@ const LibraryContract = 6
 // before it, its presence is what tells the controller this host may be sent `runner` on an identity.
 const OwnGroupContract = 7
 
+// BusyContract is the statement of a host that also reads a container's `busy` (novox/hq ADR 0335): it asks a
+// container that declares it before replacing it, leaves it running while it says busy, within a bound of
+// 15 minutes, and says the wait in its report's `busy`. Like the fields before it, its presence is what tells
+// the controller this host may be sent `busy` on a container; an older host refuses the whole declaration
+// for it.
+const BusyContract = 8
+
 // Health is one statement of every long-running resource's state on this machine (to-be 48 §4). Said in
 // every report, as an event on each change, and again every minute while anything is not healthy — so a
 // lost statement is not a lost fault.
@@ -731,6 +746,17 @@ type Window struct {
 	Until time.Time `json:"until"`
 }
 
+// Busy is one container a busy command held (novox/hq ADR 0335), as a report says it. ID is the resource's
+// id, `<module>.<resource>`.
+type Busy struct {
+	ID        string    `json:"id"`
+	Container string    `json:"container"`
+	State     string    `json:"state"`
+	Since     time.Time `json:"since"`
+	Until     time.Time `json:"until"`
+	Said      string    `json:"said,omitempty"`
+}
+
 // A Stray is a container the mesh neither wrote nor holds (ADR 0163).
 type Stray struct {
 	Kind   string `json:"kind"`
diff --git a/internal/store/store.go b/internal/store/store.go
index 5bdd2a4..3726606 100644
--- a/internal/store/store.go
+++ b/internal/store/store.go
@@ -155,6 +155,11 @@ type Applied struct {
 	// container's spec label; this is the same information kept per file, so that when the spec
 	// no longer matches the host can say WHICH file changed rather than only that something did.
 	Reads map[string]string `json:"reads,omitempty"`
+
+	// BusySince is, for a container left running because it said busy, when the first apply that would
+	// have replaced it ran (novox/hq ADR 0335 §3): kept here, beside the machine's state, so the bound runs
+	// from then across every pass and across a restart of the node-engine. Absent while nothing waits.
+	BusySince *time.Time `json:"busy_since,omitempty"`
 }
 
 // Into is what a file written into held before the mesh's keys, or before the mesh's block.