diff --git a/GPy/kern/_src/prod.py b/GPy/kern/_src/prod.py
index dd9a5fe4..e3776838 100644
--- a/GPy/kern/_src/prod.py
+++ b/GPy/kern/_src/prod.py
@@ -5,6 +5,7 @@ import numpy as np
 from kern import CombinationKernel
 from ...util.caching import Cache_this
 import itertools
+import operator
 
 class Prod(CombinationKernel):
     """
@@ -42,9 +43,19 @@ class Prod(CombinationKernel):
         return reduce(np.multiply, (p.Kdiag(X) for p in which_parts))
 
     def update_gradients_full(self, dL_dK, X, X2=None):
+        np.seterr(invalid='raise')
         k = self.K(X,X2)*dL_dK
-        for p in self.parts:
-            p.update_gradients_full(k/p.K(X,X2),X,X2)
+        try:
+            for p in self.parts:
+                p.update_gradients_full(k/p.K(X,X2),X,X2)
+        except FloatingPointError:
+            np.seterr(invalid='warn')
+            print "Gradient warning: falling back to slow version due to zero-valued kernel"
+            for combination in itertools.combinations(self.parts, len(self.parts) - 1):
+                prod = reduce(operator.mul, [p.K(X, X2) for p in combination])
+                to_update = list(set(self.parts) - set(combination))[0]
+                to_update.update_gradients_full(dL_dK * prod, X, X2)
+
 
     def update_gradients_diag(self, dL_dKdiag, X):
         k = self.Kdiag(X)*dL_dKdiag
diff --git a/GPy/testing/kernel_tests.py b/GPy/testing/kernel_tests.py
index c1bb9265..387047b6 100644
--- a/GPy/testing/kernel_tests.py
+++ b/GPy/testing/kernel_tests.py
@@ -400,12 +400,27 @@ class Coregionalize_weave_test(unittest.TestCase):
     #reset the weave state for any other tests
     GPy.util.config.config.set('weave', 'working', 'False')
 
+class KernelTestsProductWithZeroValues(unittest.TestCase):
+
+    def test_zero_valued_kernel(self):
+        X = np.array([[0,1],[1,0]])
+        Y = np.array([[1],[10]])
+        lin = GPy.kern.Linear(2)
+        bias = GPy.kern.Bias(2)
+        k = lin * bias
+        #k = lin
+        m = GPy.models.GPRegression(X, Y, kernel=k)
+        #m['mul.bias.variance'].constrain_fixed(0)
+        m.optimize(messages=False)
 
 
 
 if __name__ == "__main__":
     print "Running unit tests, please be (very) patient..."
     unittest.main()
+    #suite = unittest.TestLoader().loadTestsFromTestCase(KernelTestsProductWithZeroValues)
+    #unittest.TextTestRunner().run(suite)
+
 #     np.random.seed(0)
 #     N0 = 3
 #     N1 = 9