diff --git a/moto/swf/exceptions.py b/moto/swf/exceptions.py
index abeb348b7..a2e12fd73 100644
--- a/moto/swf/exceptions.py
+++ b/moto/swf/exceptions.py
@@ -119,3 +119,8 @@ class SWFDecisionValidationException(SWFClientError):
             prefix.format(count) + "; ".join(messages),
             "com.amazon.coral.validate#ValidationException"
         )
+
+
+class SWFWorkflowExecutionClosedError(Exception):
+    def __str__(self):
+        return repr("Cannot change this object because the WorkflowExecution is closed")
diff --git a/moto/swf/models/activity_task.py b/moto/swf/models/activity_task.py
index 91f6f0b21..1f011cb8d 100644
--- a/moto/swf/models/activity_task.py
+++ b/moto/swf/models/activity_task.py
@@ -2,6 +2,7 @@ from __future__ import unicode_literals
 from datetime import datetime
 import uuid
 
+from ..exceptions import SWFWorkflowExecutionClosedError
 from ..utils import now_timestamp
 
 
@@ -24,6 +25,10 @@ class ActivityTask(object):
         # but that shouldn't be a problem for tests
         self.scheduled_at = datetime.now()
 
+    def _check_workflow_execution_open(self):
+        if not self.workflow_execution.open:
+            raise SWFWorkflowExecutionClosedError()
+
     @property
     def open(self):
         return self.state in ["SCHEDULED", "STARTED"]
@@ -45,9 +50,11 @@ class ActivityTask(object):
         self.started_event_id = started_event_id
 
     def complete(self):
+        self._check_workflow_execution_open()
         self.state = "COMPLETED"
 
     def fail(self):
+        self._check_workflow_execution_open()
         self.state = "FAILED"
 
     def reset_heartbeat_clock(self):
@@ -63,5 +70,9 @@ class ActivityTask(object):
 
     def process_timeouts(self):
         if self.has_timedout():
-            self.state = "TIMED_OUT"
-            self.timeout_type = "HEARTBEAT"
+            self.timeout()
+
+    def timeout(self):
+        self._check_workflow_execution_open()
+        self.state = "TIMED_OUT"
+        self.timeout_type = "HEARTBEAT"
diff --git a/moto/swf/models/decision_task.py b/moto/swf/models/decision_task.py
index d024ae118..23822976c 100644
--- a/moto/swf/models/decision_task.py
+++ b/moto/swf/models/decision_task.py
@@ -2,6 +2,7 @@ from __future__ import unicode_literals
 from datetime import datetime
 import uuid
 
+from ..exceptions import SWFWorkflowExecutionClosedError
 from ..utils import now_timestamp
 
 
@@ -21,6 +22,10 @@ class DecisionTask(object):
         self.scheduled_at = datetime.now()
         self.timeout_type = None
 
+    def _check_workflow_execution_open(self):
+        if not self.workflow_execution.open:
+            raise SWFWorkflowExecutionClosedError()
+
     def to_full_dict(self, reverse_order=False):
         events = self.workflow_execution.events(reverse_order=reverse_order)
         hsh = {
@@ -42,6 +47,7 @@ class DecisionTask(object):
         self.started_event_id = started_event_id
 
     def complete(self):
+        self._check_workflow_execution_open()
         self.state = "COMPLETED"
 
     def has_timedout(self):
@@ -54,5 +60,9 @@ class DecisionTask(object):
 
     def process_timeouts(self):
         if self.has_timedout():
-            self.state = "TIMED_OUT"
-            self.timeout_type = "START_TO_CLOSE"
+            self.timeout()
+
+    def timeout(self):
+        self._check_workflow_execution_open()
+        self.state = "TIMED_OUT"
+        self.timeout_type = "START_TO_CLOSE"
diff --git a/tests/test_swf/models/test_activity_task.py b/tests/test_swf/models/test_activity_task.py
index f9f0e2ef7..8b81cbdd5 100644
--- a/tests/test_swf/models/test_activity_task.py
+++ b/tests/test_swf/models/test_activity_task.py
@@ -1,6 +1,7 @@
 from freezegun import freeze_time
 from sure import expect
 
+from moto.swf.exceptions import SWFWorkflowExecutionClosedError
 from moto.swf.models import (
     ActivityTask,
     ActivityType,
@@ -123,3 +124,21 @@ def test_activity_task_cannot_timeout_on_closed_workflow_execution():
         wfe.has_timedout().should.equal(True)
         wfe.process_timeouts()
         task.has_timedout().should.equal(False)
+
+def test_activity_task_cannot_change_state_on_closed_workflow_execution():
+    wfe = make_workflow_execution()
+    wfe.start()
+
+    task = ActivityTask(
+        activity_id="my-activity-123",
+        activity_type="foo",
+        input="optional",
+        scheduled_event_id=117,
+        timeouts=ACTIVITY_TASK_TIMEOUTS,
+        workflow_execution=wfe,
+    )
+    wfe.complete(123)
+
+    task.timeout.when.called_with().should.throw(SWFWorkflowExecutionClosedError)
+    task.complete.when.called_with().should.throw(SWFWorkflowExecutionClosedError)
+    task.fail.when.called_with().should.throw(SWFWorkflowExecutionClosedError)
diff --git a/tests/test_swf/models/test_decision_task.py b/tests/test_swf/models/test_decision_task.py
index f0efb94c0..ae2b59fdc 100644
--- a/tests/test_swf/models/test_decision_task.py
+++ b/tests/test_swf/models/test_decision_task.py
@@ -1,6 +1,7 @@
 from freezegun import freeze_time
 from sure import expect
 
+from moto.swf.exceptions import SWFWorkflowExecutionClosedError
 from moto.swf.models import DecisionTask
 
 from ..utils import make_workflow_execution
@@ -61,3 +62,13 @@ def test_decision_task_cannot_timeout_on_closed_workflow_execution():
         wfe.has_timedout().should.equal(True)
         wfe.process_timeouts()
         dt.has_timedout().should.equal(False)
+
+def test_decision_task_cannot_change_state_on_closed_workflow_execution():
+    wfe = make_workflow_execution()
+    wfe.start()
+    task = DecisionTask(wfe, 123)
+
+    wfe.complete(123)
+
+    task.timeout.when.called_with().should.throw(SWFWorkflowExecutionClosedError)
+    task.complete.when.called_with().should.throw(SWFWorkflowExecutionClosedError)