diff --git a/Lib/_abcoll.py b/Lib/_abcoll.py
index 73e668c..e7376e4 100644
--- a/Lib/_abcoll.py
+++ b/Lib/_abcoll.py
@@ -82,7 +82,7 @@
     @classmethod
     def __subclasshook__(cls, C):
         if cls is Iterator:
-            if _hasattr(C, "next"):
+            if _hasattr(C, "next") and _hasattr(C, "__iter__"):
                 return True
         return NotImplemented
 
diff --git a/Lib/test/test_collections.py b/Lib/test/test_collections.py
index 94305ab..2d2319f 100644
--- a/Lib/test/test_collections.py
+++ b/Lib/test/test_collections.py
@@ -355,8 +355,19 @@
         for x in samples:
             self.assertIsInstance(x, Iterator)
             self.assertTrue(issubclass(type(x), Iterator), repr(type(x)))
-        self.validate_abstract_methods(Iterator, 'next')
-        self.validate_isinstance(Iterator, 'next')
+        self.validate_abstract_methods(Iterator, 'next', '__iter__')
+
+        # Issue 10565
+        class NextOnly:
+            def __next__(self):
+                yield 1
+                raise StopIteration
+        self.assertNotIsInstance(NextOnly(), Iterator)
+        class NextOnlyNew(object):
+            def __next__(self):
+                yield 1
+                raise StopIteration
+        self.assertNotIsInstance(NextOnlyNew(), Iterator)
 
     def test_Sized(self):
         non_samples = [None, 42, 3.14, 1j,
diff --git a/Misc/NEWS b/Misc/NEWS
index 7bac7f4..47ddc7f 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -22,6 +22,9 @@
 Library
 -------
 
+- Issue #10565: The collections.Iterator ABC now checks for both
+  ``__iter__`` and ``next``.
+
 - Issue #10092: Properly reset locale in calendar.Locale*Calendar classes.
 
 - Issue #10459: Update CJK character names to Unicode 5.2.