diff --git a/a2a/src/main/java/com/google/adk/a2a/agent/RemoteA2AAgent.java b/a2a/src/main/java/com/google/adk/a2a/agent/RemoteA2AAgent.java
index d4e094710..5ea71de70 100644
--- a/a2a/src/main/java/com/google/adk/a2a/agent/RemoteA2AAgent.java
+++ b/a2a/src/main/java/com/google/adk/a2a/agent/RemoteA2AAgent.java
@@ -36,13 +36,13 @@
 import com.google.genai.types.Part;
 import io.a2a.client.Client;
 import io.a2a.client.ClientEvent;
+import io.a2a.client.MessageEvent;
 import io.a2a.client.TaskEvent;
 import io.a2a.client.TaskUpdateEvent;
 import io.a2a.spec.A2AClientException;
 import io.a2a.spec.AgentCard;
 import io.a2a.spec.Message;
 import io.a2a.spec.TaskArtifactUpdateEvent;
-import io.a2a.spec.TaskState;
 import io.a2a.spec.TaskStatusUpdateEvent;
 import io.reactivex.rxjava3.core.BackpressureStrategy;
 import io.reactivex.rxjava3.core.Flowable;
@@ -227,8 +227,7 @@ protected Flowable<Event> runAsyncImpl(InvocationContext invocationContext) {
     return Flowable.create(
         emitter -> {
           StreamHandler handler =
-              new StreamHandler(
-                  emitter.serialize(), invocationContext, requestJson, streaming, name());
+              new StreamHandler(emitter.serialize(), invocationContext, requestJson, name());
           ImmutableList<BiConsumer<ClientEvent, AgentCard>> consumers =
               ImmutableList.of(handler::handleEvent);
           a2aClient.sendMessage(originalMessage, consumers, handler::handleError, null);
@@ -249,7 +248,6 @@ private static class StreamHandler {
     private final FlowableEmitter<Event> emitter;
     private final InvocationContext invocationContext;
     private final String requestJson;
-    private final boolean streaming;
     private final String agentName;
     private boolean done = false;
     private final StringBuilder textBuffer = new StringBuilder();
@@ -259,12 +257,10 @@ private static class StreamHandler {
         FlowableEmitter<Event> emitter,
         InvocationContext invocationContext,
         String requestJson,
-        boolean streaming,
         String agentName) {
       this.emitter = emitter;
       this.invocationContext = invocationContext;
       this.requestJson = requestJson;
-      this.streaming = streaming;
       this.agentName = agentName;
     }
 
@@ -522,13 +518,13 @@ private Event createAggregatedEvent(Content content, @Nullable ClientEvent trigg
   }
 
   private static boolean isCompleted(ClientEvent event) {
-    TaskState executionState = TaskState.UNKNOWN;
     if (event instanceof TaskEvent taskEvent) {
-      executionState = taskEvent.getTask().getStatus().state();
-    } else if (event instanceof TaskUpdateEvent updateEvent) {
-      executionState = updateEvent.getTask().getStatus().state();
+      return taskEvent.getTask().getStatus().state().isFinal();
+    }
+    if (event instanceof TaskUpdateEvent updateEvent) {
+      return updateEvent.getTask().getStatus().state().isFinal();
     }
-    return executionState.equals(TaskState.COMPLETED);
+    return false;
   }
 
   private static ImmutableList<Part> eventParts(Event event) {
diff --git a/a2a/src/test/java/com/google/adk/a2a/agent/RemoteA2AAgentTest.java b/a2a/src/test/java/com/google/adk/a2a/agent/RemoteA2AAgentTest.java
index 8d6c9b062..91c104008 100644
--- a/a2a/src/test/java/com/google/adk/a2a/agent/RemoteA2AAgentTest.java
+++ b/a2a/src/test/java/com/google/adk/a2a/agent/RemoteA2AAgentTest.java
@@ -44,6 +44,7 @@
 import com.google.genai.types.Part;
 import io.a2a.client.Client;
 import io.a2a.client.ClientEvent;
+import io.a2a.client.MessageEvent;
 import io.a2a.client.TaskEvent;
 import io.a2a.client.TaskUpdateEvent;
 import io.a2a.spec.AgentCapabilities;
@@ -761,6 +762,24 @@ private ClientEvent createFinalEvent(String text) {
     return createTestEvent(new TextPart(text), TaskState.COMPLETED, false, false);
   }
 
+  private ClientEvent createFailedEvent(String errorMessage) {
+    return createTestEvent(new TextPart(errorMessage), TaskState.FAILED, false, false);
+  }
+
+  private ClientEvent createCanceledEvent(String message) {
+    return createTestEvent(new TextPart(message), TaskState.CANCELED, false, false);
+  }
+
+  private ClientEvent createMessageEvent(String text) {
+    Message message =
+        new Message.Builder()
+            .messageId("msg-id-1")
+            .role(Message.Role.AGENT)
+            .parts(new TextPart(text))
+            .build();
+    return new MessageEvent(message);
+  }
+
   private ClientEvent createTestEvent(
       io.a2a.spec.Part<?> part, TaskState state, boolean append, boolean lastChunk) {
     Artifact artifact =
@@ -788,6 +807,62 @@ private ClientEvent createTestEvent(
     return new TaskUpdateEvent(task, updateEvent);
   }
 
+  @Test
+  public void runAsync_terminatesOnFailureTaskState() {
+    RemoteA2AAgent agent = createAgent();
+    mockStreamResponse(
+        consumer -> {
+          consumer.accept(createPartialEvent("Processing data...", true, false), agentCard);
+          consumer.accept(createFailedEvent("Internal Server Error"), agentCard);
+        });
+
+    List<Event> events = agent.runAsync(invocationContext).toList().blockingGet();
+
+    // The stream must terminate cleanly and include the final event with error info.
+    assertThat(events).hasSize(3);
+    assertText(events.get(0), "Processing data...");
+    assertText(events.get(1), "Processing data..."); // aggregated
+    assertText(events.get(2), "Internal Server Error"); // terminal failure event
+  }
+
+  @Test
+  public void runAsync_terminatesOnCanceledTaskState() {
+    RemoteA2AAgent agent = createAgent();
+    mockStreamResponse(
+        consumer -> {
+          consumer.accept(createPartialEvent("Processing data...", true, false), agentCard);
+          consumer.accept(createCanceledEvent("Execution Canceled"), agentCard);
+        });
+
+    List<Event> events = agent.runAsync(invocationContext).toList().blockingGet();
+
+    // The stream must terminate cleanly and include the final event with cancellation info.
+    assertThat(events).hasSize(3);
+    assertText(events.get(0), "Processing data...");
+    assertText(events.get(1), "Processing data..."); // aggregated
+    assertText(events.get(2), "Execution Canceled"); // terminal canceled event
+  }
+
+  @Test
+  public void runAsync_doesNotTerminateOnMessageEvent() {
+    RemoteA2AAgent agent = createAgent();
+    mockStreamResponse(
+        consumer -> {
+          consumer.accept(createPartialEvent("Processing data...", true, false), agentCard);
+          consumer.accept(createMessageEvent("Standard chat update message"), agentCard);
+          consumer.accept(createFinalEvent("Done"), agentCard);
+        });
+
+    List<Event> events = agent.runAsync(invocationContext).toList().blockingGet();
+
+    // The stream must not terminate early on MessageEvent, and run until createFinalEvent.
+    assertThat(events).hasSize(4);
+    assertText(events.get(0), "Processing data...");
+    assertText(events.get(1), "Processing data..."); // aggregated (flushed)
+    assertText(events.get(2), "Standard chat update message"); // message event
+    assertText(events.get(3), "Done"); // terminal completed event
+  }
+
   private RemoteA2AAgent.Builder getAgentBuilder() {
     return RemoteA2AAgent.builder().name("remote-agent").a2aClient(mockClient).agentCard(agentCard);
   }