diff --git a/pyroaring/abstract_bitmap.pxi b/pyroaring/abstract_bitmap.pxi
index 1db09bc..2e7419a 100644
--- a/pyroaring/abstract_bitmap.pxi
+++ b/pyroaring/abstract_bitmap.pxi
@@ -116,6 +116,8 @@ cdef class AbstractBitMap:
             croaring.roaring_bitmap_free(self._c_bitmap)
 
     def _check_compatibility(self, AbstractBitMap other):
+        if other is None:
+            raise TypeError('Argument has incorrect type (expected pyroaring.AbstractBitMap, got None)')
         if self.copy_on_write != other.copy_on_write:
             raise ValueError('Cannot have interactions between bitmaps with and without copy_on_write.\n')
 
@@ -128,21 +130,33 @@ cdef class AbstractBitMap:
     def __len__(self):
         return croaring.roaring_bitmap_get_cardinality(self._c_bitmap)
 
-    def __richcmp__(self, other, int op):
+    def __lt__(self, AbstractBitMap other):
         self._check_compatibility(other)
-        if op == 0: # <
-            return croaring.roaring_bitmap_is_strict_subset((<AbstractBitMap?>self)._c_bitmap, (<AbstractBitMap?>other)._c_bitmap)
-        elif op == 1: # <=
-            return croaring.roaring_bitmap_is_subset((<AbstractBitMap?>self)._c_bitmap, (<AbstractBitMap?>other)._c_bitmap)
-        elif op == 2: # ==
-            return croaring.roaring_bitmap_equals((<AbstractBitMap?>self)._c_bitmap, (<AbstractBitMap?>other)._c_bitmap)
-        elif op == 3: # !=
-            return not (self == other)
-        elif op == 4: # >
-            return croaring.roaring_bitmap_is_strict_subset((<AbstractBitMap?>other)._c_bitmap, (<AbstractBitMap?>self)._c_bitmap)
-        else:         # >=
-            assert op == 5
-            return croaring.roaring_bitmap_is_subset((<AbstractBitMap?>other)._c_bitmap, (<AbstractBitMap?>self)._c_bitmap)
+        return croaring.roaring_bitmap_is_strict_subset((<AbstractBitMap?>self)._c_bitmap, (<AbstractBitMap?>other)._c_bitmap)
+
+    def __le__(self, AbstractBitMap other):
+        self._check_compatibility(other)
+        return croaring.roaring_bitmap_is_subset((<AbstractBitMap?>self)._c_bitmap, (<AbstractBitMap?>other)._c_bitmap)
+
+    def __eq__(self, object other):
+        if not isinstance(other, AbstractBitMap):
+            return NotImplemented
+        self._check_compatibility(other)
+        return croaring.roaring_bitmap_equals((<AbstractBitMap?>self)._c_bitmap, (<AbstractBitMap?>other)._c_bitmap)
+
+    def __ne__(self, object other):
+        if not isinstance(other, AbstractBitMap):
+            return NotImplemented
+        self._check_compatibility(other)
+        return not croaring.roaring_bitmap_equals((<AbstractBitMap?>self)._c_bitmap, (<AbstractBitMap?>other)._c_bitmap)
+
+    def __gt__(self, AbstractBitMap other):
+        self._check_compatibility(other)
+        return croaring.roaring_bitmap_is_strict_subset((<AbstractBitMap?>other)._c_bitmap, (<AbstractBitMap?>self)._c_bitmap)
+
+    def __ge__(self, AbstractBitMap other):
+        self._check_compatibility(other)
+        return croaring.roaring_bitmap_is_subset((<AbstractBitMap?>other)._c_bitmap, (<AbstractBitMap?>self)._c_bitmap)
 
     def contains_range(self, uint64_t range_start, uint64_t range_end):
         """
diff --git a/test.py b/test.py
index 8724c21..0131eb9 100755
--- a/test.py
+++ b/test.py
@@ -528,7 +528,7 @@ def test_comparison(
         values2: HypCollection,
         cow: bool,
     ) -> None:
-        for op in [operator.le, operator.ge, operator.lt, operator.gt]:
+        for op in [operator.le, operator.ge, operator.lt, operator.gt, operator.eq, operator.ne]:
             self.set1 = set(values1)
             self.set2 = set(values2)
             self.bitmap1 = cls1(values1, copy_on_write=cow)
@@ -542,6 +542,15 @@ def test_comparison(
             self.assertEqual(op(self.set1, self.set1 | self.set2),
                              op(self.set1, self.set1 | self.set2))
 
+    @given(bitmap_cls, hyp_collection, st.booleans())
+    def test_comparison_other_objects(self, cls: type[EitherBitMap], values: HypCollection, cow: bool) -> None:
+        for op in [operator.le, operator.ge, operator.lt, operator.gt]:
+            bm = cls(values, copy_on_write=cow)
+            with self.assertRaises(TypeError):
+                op(bm, 42)
+            with self.assertRaises(TypeError):
+                op(bm, None)
+
     @given(bitmap_cls, bitmap_cls, hyp_collection, hyp_collection, st.booleans())
     def test_intersect(
         self,
@@ -555,6 +564,24 @@ def test_intersect(
         bm2 = cls2(values2, copy_on_write=cow)
         self.assertEqual(bm1.intersect(bm2), len(bm1 & bm2) > 0)
 
+    @given(bitmap_cls, hyp_collection, st.booleans())
+    def test_eq_other_objects(self, cls: type[EitherBitMap], values: HypCollection, cow: bool) -> None:
+        bm = cls(values, copy_on_write=cow)
+
+        self.assertFalse(bm == 42)
+        self.assertIs(cls.__eq__(bm, 42), NotImplemented)
+        self.assertFalse(bm == None)  # noqa: E711
+        self.assertIs(cls.__eq__(bm, None), NotImplemented)
+
+    @given(bitmap_cls, hyp_collection, st.booleans())
+    def test_ne_other_objects(self, cls: type[EitherBitMap], values: HypCollection, cow: bool) -> None:
+        bm = cls(values, copy_on_write=cow)
+
+        self.assertTrue(bm != 42)
+        self.assertIs(cls.__ne__(bm, 42), NotImplemented)
+        self.assertTrue(bm != None)  # noqa: E711
+        self.assertIs(cls.__ne__(bm, None), NotImplemented)
+
 
 class RangeTest(Util):
     @given(bitmap_cls, hyp_collection, st.booleans(), uint32, uint32)