diff --git a/xarray/tests/test_dataset.py b/xarray/tests/test_dataset.py
index 325769c622d..7f10b4f66f7 100644
--- a/xarray/tests/test_dataset.py
+++ b/xarray/tests/test_dataset.py
@@ -1626,7 +1626,7 @@ def test_align(self):
 
         left2, right2 = align(left, right, join='outer')
         assert_equal(left2['dim3'].variable, right2['dim3'].variable)
-        assert_equal(left2['dim3'], union)
+        assert_array_equal(left2['dim3'], union)
         assert_identical(left2.sel(dim3=intersection),
                                     right2.sel(dim3=intersection))
         assert np.isnan(left2['var3'][-2:]).all()
diff --git a/xarray/tests/test_ufuncs.py b/xarray/tests/test_ufuncs.py
index 717b50602db..7449beabaf8 100644
--- a/xarray/tests/test_ufuncs.py
+++ b/xarray/tests/test_ufuncs.py
@@ -26,7 +26,7 @@ def test_unary(self):
                 xr.DataArray([0, 0], dims='x'),
                 xr.Dataset({'y': ('x', [0, 0])})]
         for a in args:
-            assert_identical(a + 1, xu.cos(a))
+            self.assertIdentical(a + 1, xu.cos(a))
 
     def test_binary(self):
         args = [0,
@@ -36,10 +36,10 @@ def test_binary(self):
                 xr.Dataset({'y': ('x', [0, 0])})]
         for n, t1 in enumerate(args):
             for t2 in args[n:]:
-                assert_identical(t2 + 1, xu.maximum(t1, t2 + 1))
-                assert_identical(t2 + 1, xu.maximum(t2, t1 + 1))
-                assert_identical(t2 + 1, xu.maximum(t1 + 1, t2))
-                assert_identical(t2 + 1, xu.maximum(t2 + 1, t1))
+                self.assertIdentical(t2 + 1, xu.maximum(t1, t2 + 1))
+                self.assertIdentical(t2 + 1, xu.maximum(t2, t1 + 1))
+                self.assertIdentical(t2 + 1, xu.maximum(t1 + 1, t2))
+                self.assertIdentical(t2 + 1, xu.maximum(t2 + 1, t1))
 
     def test_groupby(self):
         ds = xr.Dataset({'a': ('x', [0, 0, 0])}, {'c': ('x', [0, 0, 1])})
@@ -65,4 +65,4 @@ def test_groupby(self):
     def test_pickle(self):
         a = 1.0
         cos_pickled = pickle.loads(pickle.dumps(xu.cos))
-        assert_identical(cos_pickled(a), xu.cos(a))
+        self.assertIdentical(cos_pickled(a), xu.cos(a))