diff -r ede0a342ed7e Lib/concurrent/futures/_base.py
--- a/Lib/concurrent/futures/_base.py	Thu Jan 23 16:49:22 2014 +0200
+++ b/Lib/concurrent/futures/_base.py	Fri Jan 24 12:15:14 2014 -0500
@@ -181,7 +181,8 @@
 
     Returns:
         An iterator that yields the given Futures as they complete (finished or
-        cancelled).
+        cancelled). If any given Futures are duplicated, they will be returned 
+        once.
 
     Raises:
         TimeoutError: If the entire result iterator could not be generated
@@ -190,11 +191,12 @@
     if timeout is not None:
         end_time = timeout + time.time()
 
+    fs = set(fs)
     with _AcquireFutures(fs):
         finished = set(
                 f for f in fs
                 if f._state in [CANCELLED_AND_NOTIFIED, FINISHED])
-        pending = set(fs) - finished
+        pending = fs - finished
         waiter = _create_and_install_waiters(fs, _AS_COMPLETED)
 
     try:
diff -r ede0a342ed7e Lib/test/test_concurrent_futures.py
--- a/Lib/test/test_concurrent_futures.py	Thu Jan 23 16:49:22 2014 +0200
+++ b/Lib/test/test_concurrent_futures.py	Fri Jan 24 12:15:14 2014 -0500
@@ -350,6 +350,13 @@
                               SUCCESSFUL_FUTURE]),
                          completed_futures)
 
+    def test_duplicate_futures(self):
+        # Issue 20367. Duplicate futures should not raise exceptions or give
+        # duplicate responses.
+        future1 = self.executor.submit(time.sleep, 2)
+        completed = [f for f in futures.as_completed([future1,future1])]
+        self.assertEqual(len(completed), 1)
+
 
 class ThreadPoolAsCompletedTests(ThreadPoolMixin, AsCompletedTests, unittest.TestCase):
     pass