diff --git a/src/flint/test/test_all.py b/src/flint/test/test_all.py
index aca7668e..bc66da75 100644
--- a/src/flint/test/test_all.py
+++ b/src/flint/test/test_all.py
@@ -1357,6 +1357,24 @@ def test_nmod():
     assert str(G(3,5)) == "3"
     assert G(3,5).repr() == "nmod(3, 5)"
 
+    # We can compare to int and fmpz types
+    assert G(1, 5) == int(1)
+    assert G(4, 5) == int(-1)
+    assert G(1, 5) == flint.fmpz(1)
+    assert G(4, 5) == flint.fmpz(-1)
+
+    # When the modulus matches, we can compare fmpz_mod
+    R = flint.fmpz_mod_ctx(5)
+    assert G(1, 5) == R(1)
+    assert G(1, 5) != R(-1)
+    assert G(4, 5) == R(4)
+    assert G(4, 5) == R(-1)
+    # when the modulus doesnt match, everything fails
+    assert G(1, 7) != R(1)
+    assert G(1, 7) != R(-1)
+    assert G(4, 7) != R(4)
+    assert G(4, 7) != R(-1)
+
 def test_nmod_poly():
     N = flint.nmod
     P = flint.nmod_poly
diff --git a/src/flint/types/nmod.pyx b/src/flint/types/nmod.pyx
index 7bcab98a..60f78b68 100644
--- a/src/flint/types/nmod.pyx
+++ b/src/flint/types/nmod.pyx
@@ -3,6 +3,7 @@ from flint.utils.typecheck cimport typecheck
 from flint.types.fmpq cimport any_as_fmpq
 from flint.types.fmpz cimport any_as_fmpz
 from flint.types.fmpz cimport fmpz
+from flint.types.fmpz_mod cimport fmpz_mod
 from flint.types.fmpq cimport fmpq
 
 from flint.flintlib.flint cimport ulong
@@ -66,25 +67,28 @@ cdef class nmod(flint_scalar):
     def modulus(self):
         return self.mod.n
 
-    def __richcmp__(s, t, int op):
-        cdef mp_limb_t v
+    def __richcmp__(self, other, int op):
         cdef bint res
+
         if op != 2 and op != 3:
             raise TypeError("nmods cannot be ordered")
-        if typecheck(s, nmod) and typecheck(t, nmod):
-            res = ((<nmod>s).val == (<nmod>t).val) and \
-                  ((<nmod>s).mod.n == (<nmod>t).mod.n)
-            if op == 2:
-                return res
-            else:
-                return not res
-        elif typecheck(s, nmod) and typecheck(t, int):
-            res = s.val == (t % s.mod.n)
-            if op == 2:
-                return res
-            else:
-                return not res
-        return NotImplemented
+        
+        if typecheck(other, nmod):
+            res = self.val == (<nmod>other).val and \
+                  self.mod.n == (<nmod>other).mod.n
+        elif typecheck(other, int):
+            res = self.val == (other % self.mod.n)
+        elif typecheck(other, fmpz):
+            res = self.val == (int(other) % self.mod.n)
+        elif typecheck(other, fmpz_mod):
+            res = self.mod.n == (<fmpz_mod>other).ctx.modulus() and \
+                  self.val == int(other)
+        else:
+            return NotImplemented
+
+        if op == 2:
+            return res
+        return not res
 
     def __hash__(self):
         return hash((int(self.val), self.modulus))