diff --git a/RELEASE_NOTES.md b/RELEASE_NOTES.md
index ab7664401..02a8a5c72 100644
--- a/RELEASE_NOTES.md
+++ b/RELEASE_NOTES.md
@@ -17,3 +17,7 @@
 ## Bug Fixes
 
 - Fixed bug with formulas raising exception when stopped.
+
+- Fix a bug that raised `CancelledError` when actor was started with `frequenz.sdk.actor.run` and stopped.
+
+- Stop catching `BaseException` in `frequenz.sdk.actor.run`. Only `CancelledError` and `Exception` are caught now.
\ No newline at end of file
diff --git a/src/frequenz/sdk/actor/_run_utils.py b/src/frequenz/sdk/actor/_run_utils.py
index 35d85fd54..f47163b7a 100644
--- a/src/frequenz/sdk/actor/_run_utils.py
+++ b/src/frequenz/sdk/actor/_run_utils.py
@@ -38,18 +38,21 @@ async def run(*actors: Actor) -> None:
         done_tasks, pending_tasks = await asyncio.wait(
             pending_tasks, return_when=asyncio.FIRST_COMPLETED
         )
-
         # This should always be only one task, but we handle many for extra safety
         for task in done_tasks:
-            # Cancellation needs to be checked first, otherwise the other methods
-            # could raise a CancelledError
-            if task.cancelled():
+            # BackgroundService returns a BaseExceptionGroup containing multiple
+            # exceptions. The 'task.result()' statement raises these exceptions,
+            # and 'except*' is used to handle them as a group. If the task raises
+            # multiple different exceptions, 'except*' will be invoked multiple times,
+            # once for each exception group.
+            try:
+                task.result()
+            except* asyncio.CancelledError:
                 _logger.info("Actor %s: Cancelled while running.", task.get_name())
-            elif exception := task.exception():
-                _logger.error(
+            except* Exception:  # pylint: disable=broad-exception-caught
+                _logger.exception(
                     "Actor %s: Raised an exception while running.",
                     task.get_name(),
-                    exc_info=exception,
                 )
             else:
                 _logger.info("Actor %s: Finished normally.", task.get_name())
diff --git a/tests/actor/test_actor.py b/tests/actor/test_actor.py
index 96015e481..05a9f5f26 100644
--- a/tests/actor/test_actor.py
+++ b/tests/actor/test_actor.py
@@ -78,31 +78,6 @@ async def _run(self) -> None:
         print(f"{self} done (should not happen)")
 
 
-class RaiseBaseExceptionActor(BaseTestActor):
-    """A faulty actor that raises a BaseException as soon as it receives a message."""
-
-    def __init__(
-        self,
-        recv: Receiver[int],
-    ) -> None:
-        """Create an instance.
-
-        Args:
-            recv: A channel receiver for int data.
-        """
-        super().__init__(name="test")
-        self._recv = recv
-
-    async def _run(self) -> None:
-        """Start the actor and crash upon receiving a message."""
-        print(f"{self} started")
-        self.inc_restart_count()
-        async for _ in self._recv:
-            print(f"{self} is about to crash")
-            raise MyBaseException("This is a test")
-        print(f"{self} done (should not happen)")
-
-
 ACTOR_INFO = ("frequenz.sdk.actor._actor", 20)
 ACTOR_ERROR = ("frequenz.sdk.actor._actor", 40)
 RUN_INFO = ("frequenz.sdk.actor._run_utils", 20)
@@ -309,41 +284,6 @@ async def test_does_not_restart_on_normal_exit(
     ]
 
 
-async def test_does_not_restart_on_base_exception(
-    actor_auto_restart_once: None,  # pylint: disable=unused-argument
-    caplog: pytest.LogCaptureFixture,
-) -> None:
-    """Create a faulty actor and expect it not to restart because it raises a base exception."""
-    caplog.set_level("DEBUG", logger="frequenz.sdk.actor._actor")
-    caplog.set_level("DEBUG", logger="frequenz.sdk.actor._run_utils")
-
-    channel: Broadcast[int] = Broadcast(name="channel")
-
-    actor = RaiseBaseExceptionActor(channel.new_receiver())
-
-    async with asyncio.timeout(1.0):
-        await channel.new_sender().send(1)
-        # We can't use pytest.raises() here because known BaseExceptions are handled
-        # specially by pytest.
-        try:
-            await run(actor)
-        except MyBaseException as error:
-            assert str(error) == "This is a test"
-
-    assert BaseTestActor.restart_count == 0
-    assert caplog.record_tuples == [
-        (*RUN_INFO, "Starting 1 actor(s)..."),
-        (*RUN_INFO, "Actor RaiseBaseExceptionActor[test]: Starting..."),
-        (*ACTOR_INFO, "Actor RaiseBaseExceptionActor[test]: Started."),
-        (*ACTOR_ERROR, "Actor RaiseBaseExceptionActor[test]: Raised a BaseException."),
-        (
-            *RUN_ERROR,
-            "Actor RaiseBaseExceptionActor[test]: Raised an exception while running.",
-        ),
-        (*RUN_INFO, "All 1 actor(s) finished."),
-    ]
-
-
 async def test_does_not_restart_if_cancelled(
     actor_auto_restart_once: None,  # pylint: disable=unused-argument
     caplog: pytest.LogCaptureFixture,
@@ -390,6 +330,6 @@ async def cancel_actor() -> None:
         (*RUN_INFO, "Actor EchoActor[EchoActor]: Starting..."),
         (*ACTOR_INFO, "Actor EchoActor[EchoActor]: Started."),
         (*ACTOR_INFO, "Actor EchoActor[EchoActor]: Cancelled."),
-        (*RUN_ERROR, "Actor EchoActor[EchoActor]: Raised an exception while running."),
+        (*RUN_INFO, "Actor EchoActor[EchoActor]: Cancelled while running."),
         (*RUN_INFO, "All 1 actor(s) finished."),
     ]