diff --git a/uint256.go b/uint256.go
index 5faa400f..5c10cbd8 100644
--- a/uint256.go
+++ b/uint256.go
@@ -190,8 +190,12 @@ func (z *Int) AddOverflow(x, y *Int) bool {
 	return carry != 0
 }
 
-// AddMod sets z to the sum ( x+y ) mod m, and returns z
+// AddMod sets z to the sum ( x+y ) mod m, and returns z.
+// If m == 0, z is set to 0 (OBS: differs from the big.Int)
 func (z *Int) AddMod(x, y, m *Int) *Int {
+	if m.IsZero() {
+		return z.Clear()
+	}
 	if z == m { // z is an alias for m  // TODO: Understand why needed and add tests for all "division" methods.
 		m = m.Clone()
 	}
@@ -567,8 +571,12 @@ func (z *Int) SMod(x, y *Int) *Int {
 }
 
 // MulMod calculates the modulo-m multiplication of x and y and
-// returns z
+// returns z.
+// If m == 0, z is set to 0 (OBS: differs from the big.Int)
 func (z *Int) MulMod(x, y, m *Int) *Int {
+	if x.IsZero() || y.IsZero() || m.IsZero() {
+		return z.Clear()
+	}
 	p := umul(x, y)
 	var (
 		pl Int
diff --git a/uint256_test.go b/uint256_test.go
index 35a17d85..ff6622fa 100644
--- a/uint256_test.go
+++ b/uint256_test.go
@@ -74,6 +74,10 @@ var (
 
 	// A collection of interesting input values for ternary operators (addmod, mulmod).
 	ternTestCases = [][3]string{
+		{"0", "0", "0"},
+		{"1", "0", "0"},
+		{"1", "1", "0"},
+		{"0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd", "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe", "0"},
 		{"0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd", "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe", "0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff"},
 		{"0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd", "3", "0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff"},
 		{"0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff", "0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff", "0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff"},
@@ -920,9 +924,22 @@ func TestTernOp(t *testing.T) {
 			}
 		}
 	}
-
-	t.Run("AddMod", func(t *testing.T) { proc(t, (*Int).AddMod, addMod) })
-	t.Run("MulMod", func(t *testing.T) { proc(t, (*Int).MulMod, mulMod) })
+	t.Run("AddMod", func(t *testing.T) {
+		proc(t, (*Int).AddMod, func(z, x, y, m *big.Int) *big.Int {
+			if m.Sign() == 0 {
+				return z.SetUint64(0)
+			}
+			return addMod(z, x, y, m)
+		})
+	})
+	t.Run("MulMod", func(t *testing.T) {
+		proc(t, (*Int).MulMod, func(z, x, y, m *big.Int) *big.Int {
+			if m.Sign() == 0 {
+				return z.SetUint64(0)
+			}
+			return mulMod(z, x, y, m)
+		})
+	})
 }
 
 func TestCmpOp(t *testing.T) {