diff --git a/src/plumpy/base/state_machine.py b/src/plumpy/base/state_machine.py
index 3400026a..c9a08848 100644
--- a/src/plumpy/base/state_machine.py
+++ b/src/plumpy/base/state_machine.py
@@ -315,7 +315,10 @@ def transition_to(self, new_state: Union[Hashable, State, Type[State]], *args: A
             # Make sure we have a state instance
             new_state = self._create_state_instance(new_state, *args, **kwargs)
             label = new_state.LABEL
-            self._exit_current_state(new_state)
+
+            # If the previous transition failed, do not try to exit it but go straight to next state
+            if not self._transition_failing:
+                self._exit_current_state(new_state)
 
             try:
                 self._enter_next_state(new_state)
diff --git a/src/plumpy/processes.py b/src/plumpy/processes.py
index 523fe2ea..41bd3609 100644
--- a/src/plumpy/processes.py
+++ b/src/plumpy/processes.py
@@ -828,6 +828,13 @@ def on_except(self, exc_info: Tuple[Any, Exception, TracebackType]) -> None:
         """Entering the EXCEPTED state."""
         exception = exc_info[1]
         exception.__traceback__ = exc_info[2]
+
+        # It is possible that we already got into a finished state and the future result was set, in which case, we
+        # should reset it before setting the exception or else ``asyncio`` will raise an exception.
+        future = self.future()
+
+        if future.done():
+            self._future = persistence.SavableFuture(loop=self._loop)
         self.future().set_exception(exception)
 
     @super_check
diff --git a/test/test_processes.py b/test/test_processes.py
index 7df907ed..e357fc4d 100644
--- a/test/test_processes.py
+++ b/test/test_processes.py
@@ -654,6 +654,40 @@ def test_execute_twice(self):
         with self.assertRaises(plumpy.ClosedError):
             proc.execute()
 
+    def test_exception_during_on_entered(self):
+        """Test that an exception raised during ``on_entered`` will cause the process to be excepted."""
+
+        class RaisingProcess(Process):
+
+            def on_entered(self, from_state):
+                if from_state is not None and from_state.label == ProcessState.RUNNING:
+                    raise RuntimeError('exception during on_entered')
+                super().on_entered(from_state)
+
+        process = RaisingProcess()
+
+        with self.assertRaises(RuntimeError):
+            process.execute()
+
+        assert not process.is_successful
+        assert process.is_excepted
+        assert str(process.exception()) == 'exception during on_entered'
+
+    def test_exception_during_run(self):
+
+        class RaisingProcess(Process):
+
+            def run(self):
+                raise RuntimeError('exception during run')
+
+        process = RaisingProcess()
+
+        with self.assertRaises(RuntimeError):
+            process.execute()
+
+        assert process.is_excepted
+        assert str(process.exception()) == 'exception during run'
+
 
 @plumpy.auto_persist('steps_ran')
 class SavePauseProc(plumpy.Process):