diff --git a/django/contrib/admin/tests.py b/django/contrib/admin/tests.py
index a8ece9d381..93191f6a0d 100644
--- a/django/contrib/admin/tests.py
+++ b/django/contrib/admin/tests.py
@@ -22,22 +22,18 @@ class AdminSeleniumWebDriverTestCase(StaticLiveServerCase):
         if not os.environ.get('DJANGO_SELENIUM_TESTS', False):
             raise SkipTest('Selenium tests not requested')
         try:
-            webdriver_class = import_by_path(cls.webdriver_class)
-        except ImportError as e:
-            raise SkipTest('Selenium webdriver "%s" not installed: %s'
-                            % (cls.webdriver_class, str(e)))
-        super(AdminSeleniumWebDriverTestCase, cls).setUpClass()
-        try:
-            cls.selenium = webdriver_class()
+            cls.selenium = import_by_path(cls.webdriver_class)()
         except Exception as e:
-            raise SkipTest('Selenium webdriver "%s" not operational: %s'
-                           % (cls.webdriver_class, str(e)))
+            raise SkipTest('Selenium webdriver "%s" not installed or not '
+                           'operational: %s' % (cls.webdriver_class, str(e)))
+        # This has to be last to ensure that resources are cleaned up properly!
+        super(AdminSeleniumWebDriverTestCase, cls).setUpClass()
 
     @classmethod
-    def tearDownClass(cls):
+    def _tearDownClassInternal(cls):
+        super(AdminSeleniumWebDriverTestCase, cls)._tearDownClassInternal()
         if hasattr(cls, 'selenium'):
             cls.selenium.quit()
-        super(AdminSeleniumWebDriverTestCase, cls).tearDownClass()
 
     def wait_until(self, callback, timeout=10):
         """
diff --git a/django/test/testcases.py b/django/test/testcases.py
index bc73496801..caff63039a 100644
--- a/django/test/testcases.py
+++ b/django/test/testcases.py
@@ -1125,12 +1125,15 @@ class LiveServerTestCase(TransactionTestCase):
         # Wait for the live server to be ready
         cls.server_thread.is_ready.wait()
         if cls.server_thread.error:
+            # Clean up behind ourselves, since tearDownClass won't get called in
+            # case of errors.
+            cls._tearDownClassInternal()
             raise cls.server_thread.error
 
         super(LiveServerTestCase, cls).setUpClass()
 
     @classmethod
-    def tearDownClass(cls):
+    def _tearDownClassInternal(cls):
         # There may not be a 'server_thread' attribute if setUpClass() for some
         # reasons has raised an exception.
         if hasattr(cls, 'server_thread'):
@@ -1143,4 +1146,7 @@ class LiveServerTestCase(TransactionTestCase):
                 and conn.settings_dict['NAME'] == ':memory:'):
                 conn.allow_thread_sharing = False
 
+    @classmethod
+    def tearDownClass(cls):
+        cls._tearDownClassInternal()
         super(LiveServerTestCase, cls).tearDownClass()