@@ -671,6 +671,34 @@ def __add__(self, other):
         else:
             raise OperandTypeError(self, other)
 
+    def _tai_difference(self, other):
+        """If other is of same class as self, return difference in TAI.
+        Otherwise, raise OperandTypeError.
+        """
+        if other.__class__ is not self.__class__:
+            raise OperandTypeError(self, other)
+        self_tai = self.tai
+        other_tai = other.tai
+        return (self_tai.jd1 - other_tai.jd1) + (self_tai.jd2 - other_tai.jd2)
+
+    def __lt__(self, other):
+        return self._tai_difference(other) < 0.
+
+    def __le__(self, other):
+        return self._tai_difference(other) <= 0.
+
+    def __eq__(self, other):
+        return self._tai_difference(other) == 0.
+
+    def __ne__(self, other):
+        return self._tai_difference(other) != 0.
+
+    def __gt__(self, other):
+        return self._tai_difference(other) > 0.
+
+    def __ge__(self, other):
+        return self._tai_difference(other) >= 0.
+
 
 class TimeDelta(Time):
     """
 
@@ -0,0 +1,50 @@
+# Licensed under a 3-clause BSD style license - see LICENSE.rst
+import numpy as np
+
+from ...tests.helper import pytest
+from .. import Time, TimeDelta, OperandTypeError
+
+
+class TestTimeComparisons():
+    """Test Comparisons of Time and TimeDelta classes"""
+
+    def setup(self):
+        self.t1 = Time(np.arange(49995,50005), format='mjd', scale='utc')
+        self.t2 = Time(np.arange(49000,51000,200), format='mjd', scale='utc')
+
+    def test_time(self):
+        t1_lt_t2 = self.t1 < self.t2
+        assert np.all(t1_lt_t2 == np.array([False, False, False, False, False,
+                                            False,True, True, True, True]))
+        t1_ge_t2 = self.t1 >= self.t2
+        assert np.all(t1_ge_t2 != t1_lt_t2)
+
+        t1_le_t2 = self.t1 <= self.t2
+        assert np.all(t1_le_t2 == np.array([False, False, False, False, False,
+                                            True,True, True, True, True]))
+        t1_gt_t2 = self.t1 > self.t2
+        assert np.all(t1_gt_t2 != t1_le_t2)
+
+        t1_eq_t2 = self.t1 == self.t2
+        assert np.all(t1_eq_t2 == np.array([False, False, False, False, False,
+                                            True, False, False, False, False]))
+        t1_ne_t2 = self.t1 != self.t2
+        assert np.all(t1_ne_t2 != t1_eq_t2)
+
+        t1_0_gt_t2_0 = self.t1[0] > self.t2[0]
+        assert t1_0_gt_t2_0 is True
+        t1_0_gt_t2 = self.t1[0] > self.t2
+        assert np.all(t1_0_gt_t2 == np.array([True, True, True, True, True,
+                                              False, False, False, False,
+                                              False]))
+        t1_gt_t2_0 = self.t1 > self.t2[0]
+        assert np.all(t1_gt_t2_0 == np.array([True, True, True, True, True,
+                                              True, True, True, True, True]))
+
+    def test_timedelta(self):
+        dt = self.t2 - self.t1
+        with pytest.raises(OperandTypeError):
+            self.t1 > dt
+        dt_gt_td0 = dt > TimeDelta(0., format='sec')
+        assert np.all(dt_gt_td0 == np.array([False, False, False, False, False,
+                                             False, True, True, True, True]))