diff --git a/GPy/testing/prior_tests.py b/GPy/testing/prior_tests.py
new file mode 100644
index 00000000..b3e3a440
--- /dev/null
+++ b/GPy/testing/prior_tests.py
@@ -0,0 +1,61 @@
+# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+import unittest
+import numpy as np
+import GPy
+
+class PriorTests(unittest.TestCase):
+    def test_lognormal(self):
+        xmin, xmax = 1, 2.5*np.pi
+        b, C, SNR = 1, 0, 0.1
+        X = np.linspace(xmin, xmax, 500)
+        y  = b*X + C + 1*np.sin(X)
+        y += 0.05*np.random.randn(len(X))
+        X, y = X[:, None], y[:, None]
+        m = GPy.models.GP_regression(X, y)
+        m.ensure_default_constraints()
+        lognormal = GPy.priors.log_Gaussian(1, 2)
+        m.set_prior('rbf', lognormal)
+        m.randomize()
+        self.assertTrue(m.checkgrad())
+
+    def test_gamma(self):
+        xmin, xmax = 1, 2.5*np.pi
+        b, C, SNR = 1, 0, 0.1
+        X = np.linspace(xmin, xmax, 500)
+        y  = b*X + C + 1*np.sin(X)
+        y += 0.05*np.random.randn(len(X))
+        X, y = X[:, None], y[:, None]
+        m = GPy.models.GP_regression(X, y)
+        m.ensure_default_constraints()
+        gamma = GPy.priors.gamma(1, 1)
+        m.set_prior('rbf', gamma)
+        m.randomize()
+        self.assertTrue(m.checkgrad())
+
+    def test_incompatibility(self):
+        xmin, xmax = 1, 2.5*np.pi
+        b, C, SNR = 1, 0, 0.1
+        X = np.linspace(xmin, xmax, 500)
+        y  = b*X + C + 1*np.sin(X)
+        y += 0.05*np.random.randn(len(X))
+        X, y = X[:, None], y[:, None]
+        m = GPy.models.GP_regression(X, y)
+        m.ensure_default_constraints()
+        gaussian = GPy.priors.Gaussian(1, 1)
+        success = False
+
+        # setting a Gaussian prior on non-negative parameters
+        # should raise an assertionerror.
+        try:
+            m.set_prior('rbf', gaussian)
+        except AssertionError:
+            success = True
+
+        self.assertTrue(success)
+
+
+if __name__ == "__main__":
+    print "Running unit tests, please be (very) patient..."
+    unittest.main()