Index: Lib/posixpath.py
===================================================================
--- Lib/posixpath.py	(revision 77442)
+++ Lib/posixpath.py	(working copy)
@@ -337,7 +337,11 @@
 def abspath(path):
     """Return an absolute path."""
     if not isabs(path):
-        path = join(os.getcwd(), path)
+        if isinstance(path, unicode):
+            cwd = os.getcwdu()
+        else:
+            cwd = os.getcwd()
+        path = join(cwd, path)
     return normpath(path)
 
 
Index: Lib/ntpath.py
===================================================================
--- Lib/ntpath.py	(revision 77442)
+++ Lib/ntpath.py	(working copy)
@@ -449,7 +449,11 @@
     def abspath(path):
         """Return the absolute version of a path."""
         if not isabs(path):
-            path = join(os.getcwd(), path)
+            if isinstance(path, unicode):
+                cwd = os.getcwdu()
+            else:
+                cwd = os.getcwd()
+            path = join(cwd, path)
         return normpath(path)
 
 else:  # use native Windows method on Windows
@@ -461,6 +465,8 @@
                 path = _getfullpathname(path)
             except WindowsError:
                 pass # Bad path - return unchanged.
+        elif isinstance(path, unicode):
+            path = os.getcwdu()
         else:
             path = os.getcwd()
         return normpath(path)
Index: Lib/test/test_ntpath.py
===================================================================
--- Lib/test/test_ntpath.py	(revision 77442)
+++ Lib/test/test_ntpath.py	(working copy)
@@ -163,10 +163,29 @@
         try:
             import nt
         except ImportError:
-            pass
+            # check that the function is there even if we are not on Windows
+            ntpath.abspath
+            # XXX this needs more tests
         else:
             tester('ntpath.abspath("C:\\")', "C:\\")
+            # XXX this needs more tests
 
+            # Issue 3426: check that abspath retuns unicode when the arg is
+            # unicode and str when it's str, with both ASCII/non-ASCII
+            # str/unicode cwds
+
+            # test non absolute paths, os.getcwd/getcwdu are called
+            for cwd in (u'cwd', u'\xe7w\xf0'):
+                with test_support.TempCWD(cwd):
+                    for path in ('', 'foo', 'C:\\foo', 'f\xf2\xf2'):
+                        self.assertStr(ntpath.abspath(path))
+                    for upath in (u'', u'fuu', u'C:\\fuu', u'f\xf9\xf9'):
+                        self.assertUnicode(ntpath.abspath(upath))
+
+            # test absolute paths, os.getcwd/getcwdu are not called
+            self.assertStr(ntpath.abspath("/foo"))
+            self.assertUnicode(ntpath.abspath(u"/foo"))
+
     def test_relpath(self):
         currentdir = os.path.split(os.getcwd())[-1]
         tester('ntpath.relpath("a")', 'a')
Index: Lib/test/test_support.py
===================================================================
--- Lib/test/test_support.py	(revision 77441)
+++ Lib/test/test_support.py	(working copy)
@@ -612,6 +612,22 @@
         sys.path[:] = self.original_value
 
 
+class TempCWD(object):
+    def __init__(self, dirname='tempdir'):
+        self.dirname = os.path.join(TESTFN, dirname)
+        self._oldcwd = os.getcwd()
+
+    def __enter__(self):
+        if not os.path.exists(self.dirname):
+            os.makedirs(self.dirname)
+        os.chdir(self.dirname)
+        return self.dirname
+
+    def __exit__(self, exc, value, tb):
+        os.chdir(self._oldcwd)
+        rmtree(os.path.dirname(self.dirname))
+
+
 class TransientResource(object):
 
     """Raise ResourceDenied if an exception is raised while the context manager
Index: Lib/test/test_posixpath.py
===================================================================
--- Lib/test/test_posixpath.py	(revision 77442)
+++ Lib/test/test_posixpath.py	(working copy)
@@ -28,6 +28,12 @@
     def assertIs(self, a, b):
         self.assertTrue(a is b)
 
+    def assertStr(self, s):
+        self.assertTrue(isinstance(s, str), '%r is not str' % s)
+
+    def assertUnicode(self, s):
+        self.assertTrue(isinstance(s, unicode), '%r is not unicode' % s)
+
     def test_normcase(self):
         # Check that normcase() is idempotent
         p = "FoO/./BaR"
@@ -389,8 +395,27 @@
         self.assertRaises(TypeError, posixpath.normpath)
 
     def test_abspath(self):
-        self.assertTrue("foo" in posixpath.abspath("foo"))
+        self.assertTrue(posixpath.abspath('foo').endswith('foo'))
+        self.assertTrue(posixpath.abspath('foo/').endswith('foo'))
+        self.assertEqual(posixpath.abspath('/foo'), '/foo')
+        self.assertEqual(posixpath.abspath(''), os.getcwd())
+        self.assertEqual(posixpath.abspath(u''), os.getcwdu())
 
+        # Issue 3426: check that abspath retuns unicode when the arg is unicode
+        # and str when it's str, with both ASCII/non-ASCII str/unicode cwds
+
+        # test non absolute paths, os.getcwd/getcwdu are called
+        for cwd in (u'cwd', u'\xe7w\xf0'):
+            with test_support.TempCWD(cwd):
+                for path in ('', 'foo', '/foo', 'f\xf2\xf2'):
+                    self.assertStr(posixpath.abspath(path))
+                for upath in (u'', u'fuu', u'/fuu', u'f\xf9\xf9'):
+                    self.assertUnicode(posixpath.abspath(upath))
+
+        # test absolute paths, os.getcwd/getcwdu are not called
+        self.assertStr(posixpath.abspath("/foo"))
+        self.assertUnicode(posixpath.abspath(u"/foo"))
+
         self.assertRaises(TypeError, posixpath.abspath)
 
     def test_realpath(self):