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())