diff --git a/moto/swf/models/activity_task.py b/moto/swf/models/activity_task.py
index 76d0eac70..eef8350e2 100644
--- a/moto/swf/models/activity_task.py
+++ b/moto/swf/models/activity_task.py
@@ -63,7 +63,7 @@ class ActivityTask(object):
         self.last_heartbeat_timestamp = now_timestamp()
 
     def first_timeout(self):
-        if not self.workflow_execution.open:
+        if not self.open or not self.workflow_execution.open:
             return None
         # TODO: handle the "NONE" case
         heartbeat_timeout_at = self.last_heartbeat_timestamp + \
diff --git a/moto/swf/models/decision_task.py b/moto/swf/models/decision_task.py
index fb7b9d080..5474332a5 100644
--- a/moto/swf/models/decision_task.py
+++ b/moto/swf/models/decision_task.py
@@ -24,6 +24,10 @@ class DecisionTask(object):
         self.scheduled_at = datetime.now()
         self.timeout_type = None
 
+    @property
+    def started(self):
+        return self.state == "STARTED"
+
     def _check_workflow_execution_open(self):
         if not self.workflow_execution.open:
             raise SWFWorkflowExecutionClosedError()
@@ -53,7 +57,7 @@ class DecisionTask(object):
         self.state = "COMPLETED"
 
     def first_timeout(self):
-        if self.state != "STARTED" or not self.workflow_execution.open:
+        if not self.started or not self.workflow_execution.open:
             return None
         # TODO: handle the "NONE" case
         start_to_close_at = self.started_timestamp + int(self.start_to_close_timeout)
diff --git a/moto/swf/models/workflow_execution.py b/moto/swf/models/workflow_execution.py
index 0f619dca1..9a54f1729 100644
--- a/moto/swf/models/workflow_execution.py
+++ b/moto/swf/models/workflow_execution.py
@@ -166,7 +166,7 @@ class WorkflowExecution(object):
         # decision tasks timeouts
         for task in self.decision_tasks:
             _timeout = task.first_timeout()
-            if task.state == "STARTED" and _timeout:
+            if _timeout:
                 self.should_schedule_decision_next = True
                 task.timeout(_timeout)
                 self._add_event(
@@ -180,7 +180,7 @@ class WorkflowExecution(object):
         # activity tasks timeouts
         for task in self.activity_tasks:
             _timeout = task.first_timeout()
-            if task.open and _timeout:
+            if _timeout:
                 self.should_schedule_decision_next = True
                 task.timeout(_timeout)
                 self._add_event(