diff --git a/gc3libs/core.py b/gc3libs/core.py
index 1c3ef786..8dc94a57 100755
--- a/gc3libs/core.py
+++ b/gc3libs/core.py
@@ -1546,7 +1546,8 @@ def progress(self):
                 elif state == Run.State.TERMINATED:
                     # task changed state, mark as to remove
                     transitioned.append(index)
-                    self._terminated.append(task)
+                    if not self.forget_terminated:
+                        self._terminated.append(task)
                 else:
                     # if we got to this point, state has an invalid value
                     gc3libs.log.error(
@@ -1621,7 +1622,8 @@ def progress(self):
                 elif old_state == Run.State.RUNNING:
                     if isinstance(task, Application):
                         currently_in_flight -= 1
-                self._terminated.append(task)
+                if not self.forget_terminated:
+                    self._terminated.append(task)
                 transitioned.append(index)
             # pylint: disable=broad-except
             except Exception as err:
@@ -1676,7 +1678,8 @@ def progress(self):
                     # task changed state, mark as to remove
                     transitioned.append(index)
                 elif state == Run.State.TERMINATED:
-                    self._terminated.append(task)
+                    if not self.forget_terminated:
+                        self._terminated.append(task)
                     # task changed state, mark as to remove
                     transitioned.append(index)
             # pylint: disable=broad-except
@@ -1879,9 +1882,11 @@ def progress(self):
 
                 if self._store and task.changed:
                     self._store.save(task)
-            # remove tasks for which final output has been retrieved
-            for index in reversed(transitioned):
-                del self._terminating[index]
+            if not self.forget_terminated:
+                # remove tasks for which final output has been retrieved
+                # (only if TERMINATED tasks have not been dropped already)
+                for index in reversed(transitioned):
+                    del self._terminating[index]
 
 
     def redo(self, task, *args, **kwargs):
diff --git a/gc3libs/tests/test_engine.py b/gc3libs/tests/test_engine.py
index 4cacd244..c78ee18a 100644
--- a/gc3libs/tests/test_engine.py
+++ b/gc3libs/tests/test_engine.py
@@ -69,6 +69,27 @@ def test_engine_progress(num_jobs=1, transition_graph=None, max_iter=100):
             current_iter += 1
 
 
+def test_engine_forget_terminated(num_jobs=3, transition_graph=None, max_iter=100):
+    with temporary_engine() as engine:
+        engine.forget_terminated = True
+
+        # generate some no-op tasks
+        for n in range(num_jobs):
+            name = 'app{nr}'.format(nr=n+1)
+            engine.add(SuccessfulApp(name))
+
+        # run them all
+        current_iter = 0
+        done = engine.stats()[Run.State.TERMINATED]
+        while done < num_jobs and current_iter < max_iter:
+            engine.progress()
+            done = engine.stats()[Run.State.TERMINATED]
+            current_iter += 1
+
+        # check that they have been forgotten
+        assert not engine._terminated
+
+
 def test_engine_progress_collection():
     with temporary_engine() as engine:
         seq = SimpleSequentialTaskCollection(3)
@@ -81,6 +102,20 @@ def test_engine_progress_collection():
         assert seq.stage().execution.state == 'TERMINATED'
 
 
+def test_engine_progress_collection_and_forget_terminated():
+    with temporary_engine() as engine:
+        engine.forget_terminated = True
+
+        seq = SimpleSequentialTaskCollection(3)
+        engine.add(seq)
+
+        # run through sequence
+        while seq.execution.state != 'TERMINATED':
+            engine.progress()
+
+        assert not engine._terminated
+
+
 def test_engine_kill_SequentialTaskCollection():
     with temporary_engine() as engine:
         seq = SimpleSequentialTaskCollection(3)
diff --git a/gc3libs/workflow.py b/gc3libs/workflow.py
index f499d0da..125f493e 100755
--- a/gc3libs/workflow.py
+++ b/gc3libs/workflow.py
@@ -151,7 +151,8 @@ def update_state(self, **extra_args):
         Update the running state of all managed tasks.
         """
         for task in self.tasks:
-            self._controller.update_job_state(task, **extra_args)
+            if task.execution.state not in [Run.State.NEW, Run.State.TERMINATED]:
+                self._controller.update_job_state(task, **extra_args)
 
     def kill(self, **extra_args):
         # XXX: provide default implementation that kills all jobs?
@@ -449,7 +450,8 @@ def update_state(self, **extra_args):
 
         # update state of current task
         task = self.tasks[self._current_task]
-        task.update_state(**extra_args)
+        if task.execution.state not in [Run.State. NEW, Run.State.TERMINATED]:
+            task.update_state(**extra_args)
         gc3libs.log.debug("Task `%s` in state %s", task, task.execution.state)
 
         # now set state based on the state of current task:
@@ -862,7 +864,8 @@ def update_state(self, **extra_args):
         for task in self.tasks:
             # gc3libs.log.debug("Updating state of %s in collection %s ..."
             #                  % (task, self))
-            task.update_state(**extra_args)
+            if task.execution.state not in [Run.State.NEW, Run.State.TERMINATED]:
+                task.update_state(**extra_args)
         self.execution.state = self._state()
         if self.execution.state == Run.State.TERMINATED:
             self.execution.returncode = (0, 0)
@@ -1118,7 +1121,8 @@ def update_state(self):
         TERMINATED and `self.retry()` is `True`.
         """
         own_state_old = self.execution.state
-        self.task.update_state()
+        if self.task.execution.state not in [Run.State.NEW, Run.State.TERMINATED]:
+            self.task.update_state()
         own_state_new = self._recompute_state()
         if (self.task.execution.state == Run.State.TERMINATED
                 and own_state_old != Run.State.TERMINATED):