diff --git a/plumpy/process_states.py b/plumpy/process_states.py
index 6bb3f85f..1ff201dc 100644
--- a/plumpy/process_states.py
+++ b/plumpy/process_states.py
@@ -1,4 +1,5 @@
 # -*- coding: utf-8 -*-
+import asyncio
 from enum import Enum
 import sys
 import traceback
@@ -232,6 +233,11 @@ async def execute(self) -> State:  # type: ignore # pylint: disable=invalid-over
             except Interruption:
                 # Let this bubble up to the caller
                 raise
+            except asyncio.CancelledError:  # pylint: disable=try-except-raise
+                # note this re-raise is only required in python<=3.7,
+                # for python>=3.8 asyncio.CancelledError does not inherit from Exception,
+                # so will not be caught below
+                raise
             except Exception:  # pylint: disable=broad-except
                 excepted = self.create_state(ProcessState.EXCEPTED, *sys.exc_info()[1:])
                 return cast(State, excepted)
diff --git a/plumpy/processes.py b/plumpy/processes.py
index 5dee8210..821d6bd1 100644
--- a/plumpy/processes.py
+++ b/plumpy/processes.py
@@ -1193,6 +1193,12 @@ async def step(self) -> None:
 
             except KeyboardInterrupt:  # pylint: disable=try-except-raise
                 raise
+            except asyncio.CancelledError:  # pylint: disable=try-except-raise
+                # note this re-raise is only required in python<=3.7,
+                # where asyncio.CancelledError == concurrent.futures.CancelledError
+                # it is encountered when the run_task is cancelled
+                # for python>=3.8 asyncio.CancelledError does not inherit from Exception, so will not be caught below
+                raise
             except Exception:  # pylint: disable=broad-except
                 # Overwrite the next state to go to excepted directly
                 next_state = self.create_state(process_states.ProcessState.EXCEPTED, *sys.exc_info()[1:])