diff --git a/CHANGES/8908.bugfix.rst b/CHANGES/8908.bugfix.rst
new file mode 100644
index 00000000000..0eb450431db
--- /dev/null
+++ b/CHANGES/8908.bugfix.rst
@@ -0,0 +1 @@
+Fixed ``CancelledError`` from one cleanup context stopping other contexts from completing -- by :user:`Dreamsorcerer`.
diff --git a/aiohttp/web_app.py b/aiohttp/web_app.py
index a35ca214572..516d5e619b5 100644
--- a/aiohttp/web_app.py
+++ b/aiohttp/web_app.py
@@ -430,7 +430,7 @@ async def _on_cleanup(self, app: Application) -> None:
                 await it.__anext__()
             except StopAsyncIteration:
                 pass
-            except Exception as exc:
+            except (Exception, asyncio.CancelledError) as exc:
                 errors.append(exc)
             else:
                 errors.append(RuntimeError(f"{it!r} has more than one 'yield'"))
diff --git a/docs/web_advanced.rst b/docs/web_advanced.rst
index a4030d341be..76fc3ea57f1 100644
--- a/docs/web_advanced.rst
+++ b/docs/web_advanced.rst
@@ -1068,13 +1068,10 @@ below::
       async with client.pubsub() as pubsub:
           await pubsub.subscribe(channel)
           while True:
-              try:
-                  msg = await pubsub.get_message(ignore_subscribe_messages=True)
-                  if msg is not None:
-                      for ws in app["websockets"]:
-                          await ws.send_str("{}: {}".format(channel, msg))
-              except asyncio.CancelledError:
-                  break
+              msg = await pubsub.get_message(ignore_subscribe_messages=True)
+              if msg is not None:
+                  for ws in app["websockets"]:
+                      await ws.send_str("{}: {}".format(channel, msg))
 
 
   async def background_tasks(app):
@@ -1083,7 +1080,8 @@ below::
       yield
 
       app[redis_listener].cancel()
-      await app[redis_listener]
+      with contextlib.suppress(asyncio.CancelledError):
+          await app[redis_listener]
 
 
   app = web.Application()
diff --git a/tests/test_web_app.py b/tests/test_web_app.py
index 14e8be404db..28e67677c2b 100644
--- a/tests/test_web_app.py
+++ b/tests/test_web_app.py
@@ -1,5 +1,5 @@
 import asyncio
-from typing import Any, AsyncIterator, Callable, Iterator, NoReturn
+from typing import Any, AsyncIterator, Callable, Iterator, NoReturn, Type
 from unittest import mock
 
 import pytest
@@ -334,7 +334,10 @@ async def fail_ctx(app: web.Application) -> AsyncIterator[NoReturn]:
     assert ctx_state == "CLEAN"
 
 
-async def test_cleanup_ctx_exception_on_cleanup_multiple() -> None:
+@pytest.mark.parametrize("exc_cls", (Exception, asyncio.CancelledError))
+async def test_cleanup_ctx_exception_on_cleanup_multiple(
+    exc_cls: Type[BaseException],
+) -> None:
     app = web.Application()
     out = []
 
@@ -346,7 +349,7 @@ async def inner(app: web.Application) -> AsyncIterator[None]:
             yield None
             out.append("post_" + str(num))
             if fail:
-                raise Exception("fail_" + str(num))
+                raise exc_cls("fail_" + str(num))
 
         return inner