diff --git a/Lib/unittest/case.py b/Lib/unittest/case.py
index 9495689..9891803 100644
--- a/Lib/unittest/case.py
+++ b/Lib/unittest/case.py
@@ -490,10 +490,12 @@
                                                           safe_repr(second)))
             raise self.failureException(msg)
 
-    def assertAlmostEqual(self, first, second, places=7, msg=None):
+
+    def assertAlmostEqual(self, first, second, places=None, msg=None, delta=None):
         """Fail if the two objects are unequal as determined by their
            difference rounded to the given number of decimal places
-           (default 7) and comparing to zero.
+           (default 7) and comparing to zero, or by comparing that the
+           between the two objects is more than the given delta.
 
            Note that decimal places (from zero) are usually not the same
            as significant digits (measured from the most signficant digit).
@@ -502,31 +504,61 @@
            compare almost equal.
         """
         if first == second:
-            # shortcut for inf
+            # shortcut
             return
-        if round(abs(second-first), places) != 0:
+        if delta is not None and places is not None:
+            raise TypeError("specify delta or places not both")
+
+        if delta is not None:
+            if abs(first - second) <= delta:
+                return
+
+            standardMsg = '%s != %s within %s delta' % (safe_repr(first),
+                                                        safe_repr(second),
+                                                        safe_repr(delta))
+        else:
+            if places is None:
+                places = 7
+
+            if round(abs(second-first), places) == 0:
+                return
+
             standardMsg = '%s != %s within %r places' % (safe_repr(first),
                                                           safe_repr(second),
                                                           places)
-            msg = self._formatMessage(msg, standardMsg)
-            raise self.failureException(msg)
+        msg = self._formatMessage(msg, standardMsg)
+        raise self.failureException(msg)
 
-    def assertNotAlmostEqual(self, first, second, places=7, msg=None):
+    def assertNotAlmostEqual(self, first, second, places=None, msg=None, delta=None):
         """Fail if the two objects are equal as determined by their
            difference rounded to the given number of decimal places
-           (default 7) and comparing to zero.
+           (default 7) and comparing to zero, or by comparing that the
+           between the two objects is less than the given delta.
 
            Note that decimal places (from zero) are usually not the same
            as significant digits (measured from the most signficant digit).
 
            Objects that are equal automatically fail.
         """
-        if (first == second) or round(abs(second-first), places) == 0:
+        if delta is not None and places is not None:
+            raise TypeError("specify delta or places not both")
+        if delta is not None:
+            if not (first == second) and abs(first - second) > delta:
+                return
+            standardMsg = '%s == %s within %s delta' % (safe_repr(first),
+                                                        safe_repr(second),
+                                                        safe_repr(delta))
+        else:
+            if places is None:
+                places = 7
+            if not (first == second) and round(abs(second-first), places) != 0:
+                return
             standardMsg = '%s == %s within %r places' % (safe_repr(first),
-                                                          safe_repr(second),
-                                                          places)
-            msg = self._formatMessage(msg, standardMsg)
-            raise self.failureException(msg)
+                                                         safe_repr(second),
+                                                         places)
+
+        msg = self._formatMessage(msg, standardMsg)
+        raise self.failureException(msg)
 
     # Synonyms for assertion methods
 
diff --git a/Lib/unittest/test/test_assertions.py b/Lib/unittest/test/test_assertions.py
index 4b4e03a..5d77ce8 100644
--- a/Lib/unittest/test/test_assertions.py
+++ b/Lib/unittest/test/test_assertions.py
@@ -1,3 +1,5 @@
+import datetime
+
 import unittest
 
 
@@ -25,6 +27,28 @@
         self.assertRaises(self.failureException, self.assertNotAlmostEqual,
                           float('inf'), float('inf'))
 
+    def test_AmostEqualWithDelta(self):
+        self.assertAlmostEqual(1.1, 1.0, delta=0.5)
+        self.assertAlmostEqual(1.0, 1.1, delta=0.5)
+        self.assertNotAlmostEqual(1.1, 1.0, delta=0.05)
+        self.assertNotAlmostEqual(1.0, 1.1, delta=0.05)
+
+        self.assertRaises(self.failureException, self.assertAlmostEqual,
+                          1.1, 1.0, delta=0.05)
+        self.assertRaises(self.failureException, self.assertNotAlmostEqual,
+                          1.1, 1.0, delta=0.5)
+
+        self.assertRaises(TypeError, self.assertAlmostEqual,
+                          1.1, 1.0, places=2, delta=2)
+        self.assertRaises(TypeError, self.assertNotAlmostEqual,
+                          1.1, 1.0, places=2, delta=2)
+
+        first = datetime.datetime.now()
+        second = first + datetime.timedelta(seconds=10)
+        self.assertAlmostEqual(first, second,
+                               delta=datetime.timedelta(seconds=20))
+        self.assertNotAlmostEqual(first, second,
+                                  delta=datetime.timedelta(seconds=5))
 
     def test_assertRaises(self):
         def _raise(e):