diff --git a/GPy/kern/_src/prod.py b/GPy/kern/_src/prod.py
index b29c85eb..63b23f45 100644
--- a/GPy/kern/_src/prod.py
+++ b/GPy/kern/_src/prod.py
@@ -80,6 +80,7 @@ class Prod(CombinationKernel):
         if len(self.parts)==2:
             target += self.parts[0].gradients_X(dL_dK*self.parts[1].K(X, X2), X, X2)
             target += self.parts[1].gradients_X(dL_dK*self.parts[0].K(X, X2), X, X2)
+        else:
             for combination in itertools.combinations(self.parts, len(self.parts) - 1):
                 prod = reduce(np.multiply, [p.K(X, X2) for p in combination])
                 to_update = list(set(self.parts) - set(combination))[0]
diff --git a/GPy/testing/kernel_tests.py b/GPy/testing/kernel_tests.py
index 415cc7eb..458f5cd8 100644
--- a/GPy/testing/kernel_tests.py
+++ b/GPy/testing/kernel_tests.py
@@ -256,13 +256,23 @@ class KernelGradientTestsContinuous(unittest.TestCase):
         k.randomize()
         self.assertTrue(check_kernel_gradient_functions(k, X=self.X, X2=self.X2, verbose=verbose))
 
+    def test_Prod1(self):
+        k = GPy.kern.RBF(self.D) * GPy.kern.Linear(self.D)
+        k.randomize()
+        self.assertTrue(check_kernel_gradient_functions(k, X=self.X, X2=self.X2, verbose=verbose))
+
     def test_Prod2(self):
-        k = (GPy.kern.RBF(2, active_dims=[0,4]) * GPy.kern.Linear(self.D))
+        k = GPy.kern.RBF(2, active_dims=[0,4]) * GPy.kern.Linear(self.D)
         k.randomize()
         self.assertTrue(check_kernel_gradient_functions(k, X=self.X, X2=self.X2, verbose=verbose))
 
     def test_Prod3(self):
-        k = (GPy.kern.RBF(2, active_dims=[0,4]) * GPy.kern.Linear(self.D))
+        k = GPy.kern.RBF(self.D) * GPy.kern.Linear(self.D) * GPy.kern.Bias(self.D)
+        k.randomize()
+        self.assertTrue(check_kernel_gradient_functions(k, X=self.X, X2=self.X2, verbose=verbose))
+
+    def test_Prod4(self):
+        k = GPy.kern.RBF(2, active_dims=[0,4]) * GPy.kern.Linear(self.D) * GPy.kern.Matern32(2, active_dims=[0,1])
         k.randomize()
         self.assertTrue(check_kernel_gradient_functions(k, X=self.X, X2=self.X2, verbose=verbose))