diff --git a/ui/src/lib/live-log-buffer.test.ts b/ui/src/lib/live-log-buffer.test.ts
new file mode 100644
index 0000000000..bf18c5440f
--- /dev/null
+++ b/ui/src/lib/live-log-buffer.test.ts
@@ -0,0 +1,35 @@
+import { describe, expect, it } from "vitest";
+import { appendCapped } from "./live-log-buffer";
+
+describe("appendCapped", () => {
+  it("returns the same array reference when there is nothing to add", () => {
+    const prev = [1, 2, 3];
+    expect(appendCapped(prev, [], 10)).toBe(prev);
+  });
+
+  it("appends without trimming while under the cap", () => {
+    expect(appendCapped([1, 2], [3, 4], 10)).toEqual([1, 2, 3, 4]);
+  });
+
+  it("keeps exactly the newest `max` entries when the result overflows", () => {
+    expect(appendCapped([1, 2, 3], [4, 5], 4)).toEqual([2, 3, 4, 5]);
+  });
+
+  it("trims correctly when a single append batch is larger than the cap", () => {
+    expect(appendCapped([1], [2, 3, 4, 5, 6], 3)).toEqual([4, 5, 6]);
+  });
+
+  it("returns exactly `max` entries when the result lands on the cap", () => {
+    const result = appendCapped([1, 2], [3], 3);
+    expect(result).toEqual([1, 2, 3]);
+    expect(result.length).toBe(3);
+  });
+
+  it("does not mutate its inputs", () => {
+    const prev = [1, 2, 3];
+    const additions = [4, 5];
+    appendCapped(prev, additions, 3);
+    expect(prev).toEqual([1, 2, 3]);
+    expect(additions).toEqual([4, 5]);
+  });
+});
diff --git a/ui/src/lib/live-log-buffer.ts b/ui/src/lib/live-log-buffer.ts
new file mode 100644
index 0000000000..f1d83539d5
--- /dev/null
+++ b/ui/src/lib/live-log-buffer.ts
@@ -0,0 +1,34 @@
+/**
+ * Live agent-run transcript viewers stream stdout/stderr and structured events
+ * for the entire lifetime of a run — which can be hours. The viewer keeps every
+ * streamed line/event in React state and renders each into a rich DOM block, so
+ * an unbounded buffer becomes an unbounded live DOM tree: the tab's memory
+ * footprint climbs into the multi-GB range even while the JS heap stays small
+ * (the cost is in retained render objects and GPU layers, not JS objects).
+ *
+ * These caps bound the *live* tail retained in memory. Older output is not lost:
+ * it stays in the persisted run log on the server and remains reachable for
+ * terminated runs through the "Load more log" pagination, which is not subject
+ * to these caps.
+ */
+export const MAX_LIVE_LOG_LINES = 5_000;
+export const MAX_LIVE_EVENTS = 2_000;
+
+/**
+ * Number of transcript blocks the live "nice" view mounts. Terminated runs
+ * render in full so explicitly paginated history stays visible; live runs tail
+ * the stream, so mounting only the most recent blocks keeps the DOM (and its
+ * off-heap render memory) bounded no matter how long the run streams.
+ */
+export const LIVE_TRANSCRIPT_RENDER_LIMIT = 1_500;
+
+/**
+ * Append `additions` to `prev`, dropping the oldest entries so the result never
+ * exceeds `max`. Returns `prev` unchanged when there is nothing to add, so React
+ * state setters can bail out of a re-render, and never mutates its inputs.
+ */
+export function appendCapped<T>(prev: T[], additions: readonly T[], max: number): T[] {
+  if (additions.length === 0) return prev;
+  const next = [...prev, ...additions];
+  return next.length > max ? next.slice(next.length - max) : next;
+}
diff --git a/ui/src/pages/AgentDetail.tsx b/ui/src/pages/AgentDetail.tsx
index ab60cae756..b0564d73ca 100644
--- a/ui/src/pages/AgentDetail.tsx
+++ b/ui/src/pages/AgentDetail.tsx
@@ -87,6 +87,12 @@ import { TooltipProvider } from "@/components/ui/tooltip";
 import { Input } from "@/components/ui/input";
 import { AgentIcon, AgentIconPicker } from "../components/AgentIconPicker";
 import { RunTranscriptView, type TranscriptMode } from "../components/transcript/RunTranscriptView";
+import {
+  appendCapped,
+  LIVE_TRANSCRIPT_RENDER_LIMIT,
+  MAX_LIVE_EVENTS,
+  MAX_LIVE_LOG_LINES,
+} from "../lib/live-log-buffer";
 import {
   isUuidLike,
   type Agent,
@@ -3492,7 +3498,11 @@ function LogViewer({ run, adapterType }: { run: HeartbeatRun; adapterType: strin
     }
 
     if (parsed.length > 0) {
-      setLogLines((prev) => [...prev, ...parsed]);
+      // Live runs stream forever, so cap the retained tail. Terminated runs are
+      // paginated by the user via "Load more log" and keep their full history.
+      setLogLines((prev) =>
+        isLive ? appendCapped(prev, parsed, MAX_LIVE_LOG_LINES) : [...prev, ...parsed],
+      );
     }
   }
 
@@ -3661,7 +3671,7 @@ function LogViewer({ run, adapterType }: { run: HeartbeatRun; adapterType: strin
       try {
         const newEvents = await heartbeatsApi.events(run.id, maxSeq, 100);
         if (newEvents.length > 0) {
-          setEvents((prev) => [...prev, ...newEvents]);
+          setEvents((prev) => appendCapped(prev, newEvents, MAX_LIVE_EVENTS));
         }
       } catch {
         // ignore polling errors
@@ -3738,7 +3748,7 @@ function LogViewer({ run, adapterType }: { run: HeartbeatRun; adapterType: strin
           const streamRaw = asNonEmptyString(payload.stream);
           const stream = streamRaw === "stderr" || streamRaw === "system" ? streamRaw : "stdout";
           const ts = asNonEmptyString((payload as Record<string, unknown>).ts) ?? event.createdAt;
-          setLogLines((prev) => [...prev, { ts, stream, chunk }]);
+          setLogLines((prev) => appendCapped(prev, [{ ts, stream, chunk }], MAX_LIVE_LOG_LINES));
           return;
         }
 
@@ -3748,7 +3758,7 @@ function LogViewer({ run, adapterType }: { run: HeartbeatRun; adapterType: strin
           const key = heartbeatProgressLogLineKey(line);
           if (seenProgressLogLineKeysRef.current.has(key)) return;
           seenProgressLogLineKeysRef.current.add(key);
-          setLogLines((prev) => [...prev, line]);
+          setLogLines((prev) => appendCapped(prev, [line], MAX_LIVE_LOG_LINES));
           return;
         }
 
@@ -3785,7 +3795,7 @@ function LogViewer({ run, adapterType }: { run: HeartbeatRun; adapterType: strin
 
         setEvents((prev) => {
           if (prev.some((existing) => existing.seq === seq)) return prev;
-          return [...prev, liveEvent];
+          return appendCapped(prev, [liveEvent], MAX_LIVE_EVENTS);
         });
       };
 
@@ -3928,6 +3938,7 @@ function LogViewer({ run, adapterType }: { run: HeartbeatRun; adapterType: strin
           entries={transcript}
           mode={transcriptMode}
           streaming={isLive}
+          limit={isLive ? LIVE_TRANSCRIPT_RENDER_LIMIT : undefined}
           emptyMessage={run.logRef ? "Waiting for transcript..." : "No persisted transcript for this run."}
         />
         {hasMoreLog && (