diff --git a/CHANGELOG.rst b/CHANGELOG.rst
index bb6c11b..413537f 100644
--- a/CHANGELOG.rst
+++ b/CHANGELOG.rst
@@ -7,6 +7,7 @@ CHANGELOG
 * Fix descendant shortcut operator '//'
 * Fix text() function
 * Fix typed select of '(name)' token
+* Fix 24-hour time for DateTime
 
 `v1.2.1`_ (2019-08-30)
 ======================
diff --git a/elementpath/datatypes.py b/elementpath/datatypes.py
index fca89ef..ea08fe9 100644
--- a/elementpath/datatypes.py
+++ b/elementpath/datatypes.py
@@ -187,7 +187,10 @@ class AbstractDateTime(object):
 
     def __init__(self, year=2000, month=1, day=1, hour=0, minute=0, second=0, microsecond=0, tzinfo=None):
         if hour == 24 and minute == second == 0:
+            delta = datetime.timedelta(days=1)
             hour = 0
+        else:
+            delta = 0
 
         if 1 <= year <= 9999:
             self._year = None
@@ -203,6 +206,9 @@ class AbstractDateTime(object):
             else:
                 self._dt = datetime.datetime(6, month, day, hour, minute, second, microsecond, tzinfo)
 
+        if delta:
+            self._dt += delta
+
     def __repr__(self):
         fields = self._pattern.groupindex.keys()
         arg_string = ', '.join(
@@ -662,6 +668,8 @@ class Time(AbstractDateTime):
         r'(?P<tzinfo>Z|[+-](?:(?:0[0-9]|1[0-3]):[0-5][0-9]|14:00))?$')
 
     def __init__(self, hour=0, minute=0, second=0, microsecond=0, tzinfo=None):
+        if hour == 24 and minute == second == 0:
+            hour = 0
         super(Time, self).__init__(hour=hour, minute=minute, second=second, microsecond=microsecond, tzinfo=tzinfo)
 
     def __str__(self):
diff --git a/tests/test_datatypes.py b/tests/test_datatypes.py
index 64c0b27..a5fbca2 100644
--- a/tests/test_datatypes.py
+++ b/tests/test_datatypes.py
@@ -142,6 +142,10 @@ class DateTimeTypesTest(unittest.TestCase):
                                        "tzinfo=Timezone(datetime.timedelta(-1, 72000)))")
         self.assertEqual(str(dt), '-0100-04-13T10:30:00-04:00')
 
+    def test_24_hour_datetime(self):
+        dt = DateTime.fromstring('0000-09-19T24:00:00Z')
+        self.assertEqual(str(dt), '0000-09-20T00:00:00Z')
+
     def test_date_repr(self):
         dt = Date.fromstring('2000-10-07')
         self.assertEqual(repr(dt), "Date(2000, 10, 7)")
@@ -214,18 +218,18 @@ class DateTimeTypesTest(unittest.TestCase):
         self.assertFalse(mkdt("2002-04-02T12:00:00") == mkdt("2002-04-02T17:00:00"))
         self.assertTrue(mkdt("2002-04-02T12:00:00") == mkdt("2002-04-02T12:00:00"))
         self.assertTrue(mkdt("2002-04-02T23:00:00-04:00") == mkdt("2002-04-03T02:00:00-01:00"))
-        self.assertTrue(mkdt("1999-12-31T24:00:00") == mkdt("1999-12-31T00:00:00"))
-        self.assertTrue(mkdt("2005-04-04T24:00:00") == mkdt("2005-04-04T00:00:00"))
+        self.assertTrue(mkdt("1999-12-31T24:00:00") == mkdt("2000-01-01T00:00:00"))
+        self.assertTrue(mkdt("2005-04-04T24:00:00") == mkdt("2005-04-05T00:00:00"))
 
         self.assertTrue(mkdt("2002-04-02T12:00:00-01:00", tz) == mkdt("2002-04-02T17:00:00+04:00", tz))
         self.assertTrue(mkdt("2002-04-02T12:00:00", tz) == mkdt("2002-04-02T23:00:00+06:00", tz))
         self.assertFalse(mkdt("2002-04-02T12:00:00", tz) == mkdt("2002-04-02T17:00:00", tz))
         self.assertTrue(mkdt("2002-04-02T12:00:00", tz) == mkdt("2002-04-02T12:00:00", tz))
         self.assertTrue(mkdt("2002-04-02T23:00:00-04:00", tz) == mkdt("2002-04-03T02:00:00-01:00", tz))
-        self.assertTrue(mkdt("1999-12-31T24:00:00", tz) == mkdt("1999-12-31T00:00:00", tz))
-        self.assertTrue(mkdt("2005-04-04T24:00:00", tz) == mkdt("2005-04-04T00:00:00", tz))
+        self.assertTrue(mkdt("1999-12-31T24:00:00", tz) == mkdt("2000-01-01T00:00:00", tz))
 
-        self.assertFalse(mkdt("2005-04-04T24:00:00", tz) != mkdt("2005-04-04T00:00:00", tz))
+        self.assertTrue(mkdt("2005-04-04T24:00:00", tz) == mkdt("2005-04-05T00:00:00", tz))
+        self.assertFalse(mkdt("2005-04-04T24:00:00", tz) != mkdt("2005-04-05T00:00:00", tz))
 
         self.assertTrue(DateTime.fromstring("-1000-01-01") == DateTime.fromstring("-1000-01-01"))
         self.assertTrue(DateTime.fromstring("-10000-01-01") == DateTime.fromstring("-10000-01-01"))
diff --git a/tests/test_xpath2_parser.py b/tests/test_xpath2_parser.py
index 58c0ed4..1f632a4 100644
--- a/tests/test_xpath2_parser.py
+++ b/tests/test_xpath2_parser.py
@@ -791,7 +791,7 @@ class XPath2ParserTest(test_xpath1_parser.XPath1ParserTest):
         )
         self.check_value('xs:dateTime("2000-05-10T21:30:00+05:24")',
                          datetime.datetime(2000, 5, 10, hour=21, minute=30, tzinfo=tz1))
-        self.check_value('xs:dateTime("1999-12-31T24:00:00")', datetime.datetime(1999, 12, 31, 0, 0, tzinfo=tz0))
+        self.check_value('xs:dateTime("1999-12-31T24:00:00")', datetime.datetime(2000, 1, 1, 0, 0, tzinfo=tz0))
 
         self.wrong_value('xs:dateTime("2000-05-10t21:30:00+05:24")')
         self.wrong_value('xs:dateTime("2000-5-10T21:30:00+05:24")')
@@ -850,7 +850,7 @@ class XPath2ParserTest(test_xpath1_parser.XPath1ParserTest):
         self.check_value('fn:year-from-dateTime(xs:dateTime("1999-05-31T13:20:00-05:00"))', 1999)
         self.check_value('fn:year-from-dateTime(xs:dateTime("1999-05-31T21:30:00-05:00"))', 1999)
         self.check_value('fn:year-from-dateTime(xs:dateTime("1999-12-31T19:20:00"))', 1999)
-        self.check_value('fn:year-from-dateTime(xs:dateTime("1999-12-31T24:00:00"))', 1999)
+        self.check_value('fn:year-from-dateTime(xs:dateTime("1999-12-31T24:00:00"))', 2000)
 
     def test_month_from_datetime_function(self):
         self.check_value('fn:month-from-dateTime(xs:dateTime("1999-05-31T13:20:00-05:00"))', 5)