diff --git a/properties/test_encode_decode.py b/properties/test_encode_decode.py
index 13f63f259cf..4b9aa8928b4 100644
--- a/properties/test_encode_decode.py
+++ b/properties/test_encode_decode.py
@@ -4,8 +4,6 @@
 These ones pass, just as you'd hope!
 
 """
-from __future__ import absolute_import, division, print_function
-
 import hypothesis.extra.numpy as npst
 import hypothesis.strategies as st
 from hypothesis import given, settings
diff --git a/xarray/core/duck_array_ops.py b/xarray/core/duck_array_ops.py
index c4db95cfd4e..ac204df568f 100644
--- a/xarray/core/duck_array_ops.py
+++ b/xarray/core/duck_array_ops.py
@@ -63,19 +63,51 @@ def fail_on_dask_array_input(values, msg=None, func_name=None):
 
 around = _dask_or_eager_func('around')
 isclose = _dask_or_eager_func('isclose')
-notnull = _dask_or_eager_func('notnull', eager_module=pd)
-_isnull = _dask_or_eager_func('isnull', eager_module=pd)
+
+if hasattr(np, 'isnat') and (
+        dask_array is None or hasattr(dask_array_type, '__array_ufunc__')):
+    # np.isnat is available since NumPy 1.13, so __array_ufunc__ is always
+    # supported.
+    isnat = np.isnat
+else:
+    isnat = _dask_or_eager_func('isnull', eager_module=pd)
+isnan = _dask_or_eager_func('isnan')
+zeros_like = _dask_or_eager_func('zeros_like')
+
+
+pandas_isnull = _dask_or_eager_func('isnull', eager_module=pd)
 
 
 def isnull(data):
-    # GH837, GH861
-    # isnull fcn from pandas will throw TypeError when run on numpy structured
-    # array therefore for dims that are np structured arrays we assume all
-    # data is present
-    try:
-        return _isnull(data)
-    except TypeError:
-        return np.zeros(data.shape, dtype=bool)
+    data = asarray(data)
+    scalar_type = data.dtype.type
+    if issubclass(scalar_type, (np.datetime64, np.timedelta64)):
+        # datetime types use NaT for null
+        # note: must check timedelta64 before integers, because currently
+        # timedelta64 inherits from np.integer
+        return isnat(data)
+    elif issubclass(scalar_type, np.inexact):
+        # float types use NaN for null
+        return isnan(data)
+    elif issubclass(
+        scalar_type, (np.bool_, np.integer, np.character, np.void)
+    ):
+        # these types cannot represent missing values
+        return zeros_like(data, dtype=bool)
+    else:
+        # at this point, array should have dtype=object
+        if isinstance(data, (np.ndarray, dask_array_type)):
+            return pandas_isnull(data)
+        else:
+            # Not reachable yet, but intended for use with other duck array
+            # types. For full consistency with pandas, we should accept None as
+            # a null value as well as NaN, but it isn't clear how to do this
+            # with duck typing.
+            return data != data
+
+
+def notnull(data):
+    return ~isnull(data)
 
 
 transpose = _dask_or_eager_func('transpose')
diff --git a/xarray/tests/test_duck_array_ops.py b/xarray/tests/test_duck_array_ops.py
index b0b7cfbd943..bb22a15e227 100644
--- a/xarray/tests/test_duck_array_ops.py
+++ b/xarray/tests/test_duck_array_ops.py
@@ -178,14 +178,18 @@ def test_wrong_shape(self):
         assert not array_notnull_equiv(a, b)
 
     @pytest.mark.parametrize("val1, val2, val3, null", [
-        (1, 2, 3, None),
+        (np.datetime64('2000'),
+         np.datetime64('2001'),
+         np.datetime64('2002'),
+         np.datetime64('NaT')),
         (1., 2., 3., np.nan),
-        (1., 2., 3., None),
         ('foo', 'bar', 'baz', None),
+        ('foo', 'bar', 'baz', np.nan),
     ])
     def test_types(self, val1, val2, val3, null):
-        arr1 = np.array([val1, null, val3, null])
-        arr2 = np.array([val1, val2, null, null])
+        dtype = object if isinstance(val1, str) else None
+        arr1 = np.array([val1, null, val3, null], dtype=dtype)
+        arr2 = np.array([val1, val2, null, null], dtype=dtype)
         assert array_notnull_equiv(arr1, arr2)
 
 
@@ -432,6 +436,19 @@ def test_argmin_max_error():
         da.argmin(dim='y')
 
 
+@pytest.mark.parametrize('array', [
+    np.array([np.datetime64('2000-01-01'), np.datetime64('NaT')]),
+    np.array([np.timedelta64(1, 'h'), np.timedelta64('NaT')]),
+    np.array([0.0, np.nan]),
+    np.array([1j, np.nan]),
+    np.array(['foo', np.nan], dtype=object),
+])
+def test_isnull(array):
+    expected = np.array([False, True])
+    actual = duck_array_ops.isnull(array)
+    np.testing.assert_equal(expected, actual)
+
+
 @requires_dask
 def test_isnull_with_dask():
     da = construct_dataarray(2, np.float32, contains_nan=True, dask=True)