diff -r 85b87789f048 Lib/test/regrtest.py
--- a/Lib/test/regrtest.py	Mon Mar 17 23:16:02 2014 +0100
+++ b/Lib/test/regrtest.py	Tue Mar 18 00:14:42 2014 +0100
@@ -322,6 +322,9 @@ def _create_parser():
     group.add_argument('-F', '--forever', action='store_true',
                        help='run the specified tests in a loop, until an '
                             'error happens')
+    group.add_argument('--check-time-delta', type=float,
+                       help='delay in seconds tolerated to check max_dt in '
+                             'check_time_delta() (default: 500 ms)')
 
     parser.add_argument('args', nargs=argparse.REMAINDER,
                         help=argparse.SUPPRESS)
@@ -420,6 +423,10 @@ def _parse_args(args, **kwargs):
                     ns.use_resources.append(r)
     if ns.random_seed is not None:
         ns.randomize = True
+    if ns.check_time_delta is not None:
+        if ns.check_time_delta < 1e-9:
+            parser.error("--check-time-delta must be >= 1e-9")
+        support.check_time_delta.max_dt_delta = ns.check_time_delta * 2
 
     return ns
 
diff -r 85b87789f048 Lib/test/support/__init__.py
--- a/Lib/test/support/__init__.py	Mon Mar 17 23:16:02 2014 +0100
+++ b/Lib/test/support/__init__.py	Tue Mar 18 00:14:42 2014 +0100
@@ -2174,3 +2174,60 @@ def run_in_subinterp(code):
                                      "memory allocations")
     import _testcapi
     return _testcapi.run_in_subinterp(code)
+
+def _format_time_delta(dt):
+    abs_dt = abs(dt)
+    if abs_dt < 1e-9:
+        # abs(dt) < 1e-9
+        return '%.1f ns' % (dt * 1e9)
+    if abs_dt < 1e-6:
+        # 1e-9 < abs(dt) < 1e-6
+        return '%.1f ns' % (dt * 1e9)
+    if abs_dt < 1e-3:
+        # 1e-6 < abs(dt) < 1e-3
+        return '%.1f us' % (dt * 1e6)
+    if abs_dt < 1.0:
+        # 1e-3 < abs(dt) < 1.0
+        return '%.1f ms' % (dt * 1e3)
+    # 1.0 < abs(dt)
+    return '%.0f sec' % dt
+
+def check_time_delta(min_dt, dt, max_dt, *, clock='time', resolution=None):
+    if max_dt < min_dt:
+        raise ValueError("check_time_delta requires max_dt >= min_dt")
+
+    if min_dt <= dt <= max_dt:
+        return
+
+    if resolution is not None:
+        message = ("use a resolution of %s"
+                   % (clock, _format_time_delta(resolution)))
+    else:
+        clock_info = time.get_clock_info(clock)
+        resolution = clock_info.resolution
+        message = ("the clock %r has a resolution of %s"
+                   % (clock, _format_time_delta(resolution)))
+
+    message = ("%s; tolerate a delta of %s seconds"
+               % (message,
+                  _format_time_delta(check_time_delta.max_dt_delta)))
+
+    min_dt2 = min_dt - resolution
+    max_dt2 = max_dt + resolution + check_time_delta.max_dt_delta
+    if min_dt2 <= dt <= max_dt2:
+        return
+
+    if dt <= max_dt2:
+        # dt < min_dt <= max_dt
+        raise AssertionError("timing %s seconds < min timing %s seconds; %s"
+                             % (_format_time_delta(dt),
+                                _format_time_delta(min_dt),
+                                message))
+    else:
+        # min_dt <= max_dt < dt
+        raise AssertionError("timing %s seconds > max timing %s seconds; %s"
+                             % (_format_time_delta(dt),
+                                _format_time_delta(max_dt),
+                                message))
+
+check_time_delta.max_dt_delta = 0.500   # seconds
diff -r 85b87789f048 Lib/test/test_asyncio/test_base_events.py
--- a/Lib/test/test_asyncio/test_base_events.py	Mon Mar 17 23:16:02 2014 +0100
+++ b/Lib/test/test_asyncio/test_base_events.py	Tue Mar 18 00:14:42 2014 +0100
@@ -7,7 +7,7 @@ import sys
 import time
 import unittest
 from unittest import mock
-from test.support import IPV6_ENABLED
+from test.support import IPV6_ENABLED, check_time_delta
 
 import asyncio
 from asyncio import base_events
@@ -130,11 +130,7 @@ class BaseEventLoopTests(unittest.TestCa
         self.loop.run_forever()
         dt = self.loop.time() - t0
 
-        # 50 ms: maximum granularity of the event loop
-        self.assertGreaterEqual(dt, delay - 0.050, dt)
-        # tolerate a difference of +800 ms because some Python buildbots
-        # are really slow
-        self.assertLessEqual(dt, 0.9, dt)
+        check_time_delta(delay, dt, delay + 0.1, clock='monotonic')
 
     def test_run_once_in_executor_handle(self):
         def cb():
diff -r 85b87789f048 Lib/test/test_time.py
--- a/Lib/test/test_time.py	Mon Mar 17 23:16:02 2014 +0100
+++ b/Lib/test/test_time.py	Tue Mar 18 00:14:42 2014 +0100
@@ -394,7 +394,7 @@ class TimeTestCase(unittest.TestCase):
         dt = t2 - t1
         self.assertGreater(t2, t1)
         # Issue #20101: On some Windows machines, dt may be slightly low
-        self.assertTrue(0.45 <= dt <= 1.0, dt)
+        support.check_time_delta(0.5, dt, 0.501, clock='monotonic')
 
         # monotonic() is a monotonic but non adjustable clock
         info = time.get_clock_info('monotonic')
@@ -406,12 +406,10 @@ class TimeTestCase(unittest.TestCase):
 
     def test_process_time(self):
         # process_time() should not include time spend during a sleep
-        start = time.process_time()
+        t0 = time.process_time()
         time.sleep(0.100)
-        stop = time.process_time()
-        # use 20 ms because process_time() has usually a resolution of 15 ms
-        # on Windows
-        self.assertLess(stop - start, 0.020)
+        dt = time.process_time() - t0
+        support.check_time_delta(0.0, dt, 0.010, clock='process_time')
 
         info = time.get_clock_info('process_time')
         self.assertTrue(info.monotonic)