diff --git a/Lib/asyncio/base_futures.py b/Lib/asyncio/base_futures.py
index 5182884..bd65bee 100644
--- a/Lib/asyncio/base_futures.py
+++ b/Lib/asyncio/base_futures.py
@@ -1,17 +1,13 @@
 __all__ = ()
 
-import concurrent.futures._base
+import concurrent.futures
 import reprlib
 
 from . import format_helpers
 
-Error = concurrent.futures._base.Error
 CancelledError = concurrent.futures.CancelledError
 TimeoutError = concurrent.futures.TimeoutError
-
-
-class InvalidStateError(Error):
-    """The operation is not allowed in this state."""
+InvalidStateError = concurrent.futures.InvalidStateError
 
 
 # States for Future.
diff --git a/Lib/concurrent/futures/__init__.py b/Lib/concurrent/futures/__init__.py
index 8434fcf..d746aea 100644
--- a/Lib/concurrent/futures/__init__.py
+++ b/Lib/concurrent/futures/__init__.py
@@ -10,6 +10,7 @@
                                       ALL_COMPLETED,
                                       CancelledError,
                                       TimeoutError,
+                                      InvalidStateError,
                                       BrokenExecutor,
                                       Future,
                                       Executor,
diff --git a/Lib/concurrent/futures/_base.py b/Lib/concurrent/futures/_base.py
index 4f22f7e..d4416c6 100644
--- a/Lib/concurrent/futures/_base.py
+++ b/Lib/concurrent/futures/_base.py
@@ -53,6 +53,10 @@
     """The operation exceeded the given deadline."""
     pass
 
+class InvalidStateError(Error):
+    """The operation is not allowed in this state."""
+    pass
+
 class _Waiter(object):
     """Provides the event that wait() and as_completed() block on."""
     def __init__(self):
@@ -513,6 +517,8 @@
         Should only be used by Executor implementations and unit tests.
         """
         with self._condition:
+            if self._state in {CANCELLED, CANCELLED_AND_NOTIFIED, FINISHED}:
+                raise InvalidStateError('{}: {!r}'.format(self._state, self))
             self._result = result
             self._state = FINISHED
             for waiter in self._waiters:
@@ -526,6 +532,8 @@
         Should only be used by Executor implementations and unit tests.
         """
         with self._condition:
+            if self._state in {CANCELLED, CANCELLED_AND_NOTIFIED, FINISHED}:
+                raise InvalidStateError('{}: {!r}'.format(self._state, self))
             self._exception = exception
             self._state = FINISHED
             for waiter in self._waiters:
diff --git a/Lib/test/test_concurrent_futures.py b/Lib/test/test_concurrent_futures.py
index b258a0e..f2c28ac 100644
--- a/Lib/test/test_concurrent_futures.py
+++ b/Lib/test/test_concurrent_futures.py
@@ -1206,6 +1206,34 @@
         self.assertTrue(isinstance(f1.exception(timeout=5), OSError))
         t.join()
 
+    def test_multiple_set_result(self):
+        f = create_future(state=PENDING)
+        f.set_result(1)
+
+        with self.assertRaisesRegex(
+                futures.InvalidStateError,
+                'FINISHED: <Future at 0x[0-9a-f]+ '
+                'state=finished returned int>'
+        ):
+            f.set_result(2)
+
+        self.assertTrue(f.done())
+        self.assertEqual(f.result(), 1)
+
+    def test_multiple_set_exception(self):
+        f = create_future(state=PENDING)
+        e = ValueError()
+        f.set_exception(e)
+
+        with self.assertRaisesRegex(
+                futures.InvalidStateError,
+                'FINISHED: <Future at 0x[0-9a-f]+ '
+                'state=finished raised ValueError>'
+        ):
+            f.set_exception(Exception())
+
+        self.assertEqual(f.exception(), e)
+
 
 @test.support.reap_threads
 def test_main():