diff --git a/tests/async_engine/test_async_llm_engine.py b/tests/async_engine/test_async_llm_engine.py
index d763f2c2e07b..03494581431d 100644
--- a/tests/async_engine/test_async_llm_engine.py
+++ b/tests/async_engine/test_async_llm_engine.py
@@ -1,14 +1,19 @@
 import asyncio
 import os
+from asyncio import CancelledError
 from dataclasses import dataclass
+from typing import Optional
 
 import pytest
+import pytest_asyncio
 import torch
 
 from vllm import SamplingParams
 from vllm.config import ParallelConfig
 from vllm.engine.async_llm_engine import AsyncEngineArgs, AsyncLLMEngine
+from vllm.outputs import RequestOutput as RealRequestOutput
 
+from ..conftest import cleanup
 from ..utils import wait_for_gpu_memory_to_clear
 
 
@@ -118,15 +123,38 @@ async def test_new_requests_event():
     os.environ.pop("VLLM_ALLOW_ENGINE_USE_RAY")
 
 
-def test_asyncio_run():
+def start_engine():
     wait_for_gpu_memory_to_clear(
         devices=list(range(torch.cuda.device_count())),
         threshold_bytes=2 * 2**30,
         timeout_s=60,
     )
 
-    engine = AsyncLLMEngine.from_engine_args(
-        AsyncEngineArgs(model="facebook/opt-125m"))
+    return AsyncLLMEngine.from_engine_args(
+        AsyncEngineArgs(model="facebook/opt-125m", enforce_eager=True))
+
+
+@pytest_asyncio.fixture(scope="module")
+async def async_engine():
+    engine = await asyncio.get_event_loop().run_in_executor(executor=None,
+                                                            func=start_engine)
+    try:
+        yield engine
+    finally:
+        engine.shutdown_background_loop()
+        del engine
+        await asyncio.sleep(0.1)
+        cleanup()
+
+
+@pytest.fixture()
+def should_do_global_cleanup_after_test(request) -> bool:
+    # So we can share the async engine fixture between these tests
+    return False
+
+
+@pytest.mark.asyncio(scope="module")
+async def test_asyncio_run(async_engine):
 
     async def run(prompt: str):
         sampling_params = SamplingParams(
@@ -134,17 +162,64 @@ def test_asyncio_run():
             max_tokens=32,
         )
 
-        async for output in engine.generate(prompt,
-                                            sampling_params,
-                                            request_id=prompt):
+        async for output in async_engine.generate(prompt,
+                                                  sampling_params,
+                                                  request_id=prompt):
             final_output = output
         return final_output
 
-    async def generate():
-        return await asyncio.gather(
-            run("test0"),
-            run("test1"),
-        )
-
-    results = asyncio.run(generate())
+    results = await asyncio.gather(
+        run("test0"),
+        run("test1"),
+    )
     assert len(results) == 2
+
+
+@pytest.mark.asyncio(scope="module")
+async def test_cancellation(async_engine):
+    sampling_params = SamplingParams(
+        temperature=0,
+        min_tokens=10,
+        max_tokens=10,
+    )
+
+    i = 0
+    with pytest.raises(CancelledError):
+        async for output in async_engine.generate("test2",
+                                                  sampling_params,
+                                                  request_id="test2"):
+            assert not output.finished
+            i += 1
+            if i == 5:
+                await async_engine.abort("test2")
+
+    assert i == 5
+
+
+@pytest.mark.asyncio(scope="module")
+async def test_delayed_generator(async_engine):
+    sampling_params = SamplingParams(
+        temperature=0,
+        min_tokens=10,
+        max_tokens=10,
+    )
+
+    stream = async_engine.generate("test3",
+                                   sampling_params,
+                                   request_id="test3")
+    i = 0
+    final_output: Optional[RealRequestOutput] = None
+    async for output in stream:
+        final_output = output
+        if i == 0:
+            # wait for generation to complete before consuming
+            # the remaining messages
+            await asyncio.sleep(1)
+        if i < 9:
+            assert not output.finished
+        i += 1
+
+    assert i == 10
+    assert final_output is not None
+    assert len(final_output.outputs[0].token_ids) == 10
+    assert final_output.finished
diff --git a/vllm/engine/async_llm_engine.py b/vllm/engine/async_llm_engine.py
index b33c19e97141..ceda0b83a239 100644
--- a/vllm/engine/async_llm_engine.py
+++ b/vllm/engine/async_llm_engine.py
@@ -2,8 +2,8 @@ import asyncio
 import time
 from dataclasses import dataclass
 from functools import partial
-from typing import (AsyncGenerator, Callable, Dict, Iterable, List, Mapping,
-                    Optional, Set, Tuple, Type, Union)
+from typing import (Any, AsyncGenerator, Callable, Dict, Iterable, List,
+                    Mapping, Optional, Set, Tuple, Type, Union)
 
 import torch
 from typing_extensions import assert_never
@@ -85,9 +85,8 @@ class AsyncStream:
 
     def put(self, item: Union[RequestOutput, EmbeddingRequestOutput,
                               Exception]) -> None:
-        if self._finished:
-            return
-        self._queue.put_nowait(item)
+        if not self._finished:
+            self._queue.put_nowait(item)
 
     def finish(
         self,
@@ -96,7 +95,7 @@ class AsyncStream:
         if not self._finished:
             self._finished = True
             self._queue.put_nowait(
-                exception if exception is not None else STOP_ITERATION)
+                exception if self._is_raisable(exception) else STOP_ITERATION)
 
     @property
     def finished(self) -> bool:
@@ -106,9 +105,9 @@ class AsyncStream:
         self
     ) -> AsyncGenerator[Union[RequestOutput, EmbeddingRequestOutput], None]:
         try:
-            while not self._finished:
+            while True:
                 result = await self._queue.get()
-                if isinstance(result, Exception):
+                if self._is_raisable(result):
                     if result == STOP_ITERATION:
                         return
                     raise result
@@ -117,6 +116,12 @@ class AsyncStream:
             self._cancel(self.request_id)
             raise asyncio.CancelledError from None
 
+    @staticmethod
+    def _is_raisable(value: Any):
+        return isinstance(value, BaseException) or \
+                (isinstance(value, type) and \
+                 issubclass(value, BaseException))
+
 
 class RequestTracker:
     """Synchronous abstraction for tracking requests."""