See https://github.com/simonpercivall/orderedset/pull/22.

--- a/lib/orderedset/_orderedset.pyx
+++ b/lib/orderedset/_orderedset.pyx
@@ -499,13 +499,15 @@ class OrderedSet(_OrderedSet, MutableSet
         return NotImplemented
 
     def __ge__(self, other):
-        ret = self < other
-        if ret is NotImplemented:
-            return ret
-        return not ret
+        if isinstance(other, Set):
+            return len(self) >= len(other) and set(self) >= set(other)
+        elif isinstance(other, list):
+            return len(self) >= len(other) and list(self) >= list(other)
+        return NotImplemented
 
     def __gt__(self, other):
-        ret = self <= other
-        if ret is NotImplemented:
-            return ret
-        return not ret
+        if isinstance(other, Set):
+            return len(self) > len(other) and set(self) > set(other)
+        elif isinstance(other, list):
+            return len(self) > len(other) and list(self) > list(other)
+        return NotImplemented
--- a/tests/test_orderedset.py
+++ b/tests/test_orderedset.py
@@ -371,6 +371,20 @@ class TestOrderedset(unittest.TestCase):
         self.assertGreater(oset1, set(oset3))
         self.assertGreater(oset1, list(oset3))
 
+        oset4 = OrderedSet(self.lst[1:])
+
+        self.assertFalse(oset3 < oset4)
+        self.assertFalse(oset3 < set(oset4))
+        self.assertFalse(oset3 < list(oset4))
+        self.assertFalse(oset3 >= oset4)
+        self.assertFalse(oset3 >= set(oset4))
+        self.assertFalse(oset3 >= list(oset4))
+        self.assertFalse(oset3 < oset4)
+        self.assertFalse(oset3 < set(oset4))
+        self.assertFalse(oset3 < list(oset4))
+        self.assertFalse(oset3 >= oset4)
+        self.assertFalse(oset3 >= set(oset4))
+        self.assertFalse(oset3 >= list(oset4))
 
 if __name__ == '__main__':
     unittest.main()