diff --git a/Lib/test/test_httplib.py b/Lib/test/test_httplib.py
index 426995b..7dae65d 100644
--- a/Lib/test/test_httplib.py
+++ b/Lib/test/test_httplib.py
@@ -317,6 +317,33 @@
         self.assertEqual("Basic realm=\"example\"",
                          resp.getheader("www-authenticate"))
 
+    # Test lines overflowing the max line size (_MAXLINE in http.client)
+
+    def test_overflowing_status_line(self):
+        body = "HTTP/1.1 200 Ok" + "k" * 65536 + "\r\n"
+        resp = client.HTTPResponse(FakeSocket(body))
+        self.assertRaises((client.LineTooLong, client.BadStatusLine), resp.begin)
+
+    def test_overflowing_header_line(self):
+        body = (
+            'HTTP/1.1 200 OK\r\n'
+            'X-Foo: bar' + 'r' * 65536 + '\r\n\r\n'
+        )
+        resp = client.HTTPResponse(FakeSocket(body))
+        self.assertRaises(client.LineTooLong, resp.begin)
+
+    def test_overflowing_chunked_line(self):
+        body = (
+            'HTTP/1.1 200 OK\r\n'
+            'Transfer-Encoding: chunked\r\n\r\n'
+            + '0' * 65536 + 'a\r\n'
+            'hello world\r\n'
+            '0\r\n'
+        )
+        resp = client.HTTPResponse(FakeSocket(body))
+        resp.begin()
+        self.assertRaises(client.LineTooLong, resp.read)
+
 class OfflineTest(TestCase):
     def test_responses(self):
         self.assertEqual(client.responses[client.NOT_FOUND], "Not Found")
diff --git a/Lib/test/test_httpservers.py b/Lib/test/test_httpservers.py
index 85b5ec4..19d3d17 100644
--- a/Lib/test/test_httpservers.py
+++ b/Lib/test/test_httpservers.py
@@ -573,6 +573,13 @@
         self.assertEqual(result[0], b'HTTP/1.1 414 Request-URI Too Long\r\n')
         self.assertFalse(self.handler.get_called)
 
+    def test_header_length(self):
+        # Issue #6791: same for headers
+        result = self.send_typical_request(
+            b'GET / HTTP/1.1\r\nX-Foo: bar' + b'r' * 65537 + b'\r\n\r\n')
+        self.assertEqual(result[0], b'HTTP/1.1 400 Line too long\r\n')
+        self.assertFalse(self.handler.get_called)
+
 class SimpleHTTPRequestHandlerTestCase(unittest.TestCase):
     """ Test url parsing """
     def setUp(self):