diff --git a/Lib/http/client.py b/Lib/http/client.py
index 7c97560..8ea75ce 100644
--- a/Lib/http/client.py
+++ b/Lib/http/client.py
@@ -203,6 +203,9 @@
 # maximal amount of data to read at one time in _safe_read
 MAXAMOUNT = 1048576
 
+# maximal line length when calling readline().
+_MAXLINE = 65536
+
 class HTTPMessage(email.message.Message):
     # XXX The only usage of this method is in
     # http.server.CGIHTTPRequestHandler.  Maybe move the code there so
@@ -245,7 +248,9 @@
     """
     headers = []
     while True:
-        line = fp.readline()
+        line = fp.readline(_MAXLINE + 1)
+        if len(line) > _MAXLINE:
+            raise LineTooLong("header line")
         headers.append(line)
         if line in (b'\r\n', b'\n', b''):
             break
@@ -299,7 +304,9 @@
         self.will_close = _UNKNOWN      # conn will close at end of response
 
     def _read_status(self):
-        line = str(self.fp.readline(), "iso-8859-1")
+        line = str(self.fp.readline(_MAXLINE + 1), "iso-8859-1")
+        if len(line) > _MAXLINE:
+            raise LineTooLong("status line")
         if self.debuglevel > 0:
             print("reply:", repr(line))
         if not line:
@@ -340,7 +347,10 @@
                 break
             # skip the header from the 100 response
             while True:
-                skip = self.fp.readline().strip()
+                skip = self.fp.readline(_MAXLINE + 1)
+                if len(skip) > _MAXLINE:
+                    raise LineTooLong("header line")
+                skip = skip.strip()
                 if not skip:
                     break
                 if self.debuglevel > 0:
@@ -508,7 +518,9 @@
         value = []
         while True:
             if chunk_left is None:
-                line = self.fp.readline()
+                line = self.fp.readline(_MAXLINE + 1)
+                if len(line) > _MAXLINE:
+                    raise LineTooLong("chunk size")
                 i = line.find(b";")
                 if i >= 0:
                     line = line[:i] # strip chunk-extensions
@@ -543,7 +555,9 @@
         # read and discard trailer up to the CRLF terminator
         ### note: we shouldn't have any trailers!
         while True:
-            line = self.fp.readline()
+            line = self.fp.readline(_MAXLINE + 1)
+            if len(line) > _MAXLINE:
+                raise LineTooLong("trailer line")
             if not line:
                 # a vanishingly small number of sites EOF without
                 # sending the trailer
@@ -692,7 +706,9 @@
             raise socket.error("Tunnel connection failed: %d %s" % (code,
                                                                     message.strip()))
         while True:
-            line = response.fp.readline()
+            line = response.fp.readline(_MAXLINE + 1)
+            if len(line) > _MAXLINE:
+                raise LineTooLong("header line")
             if line == b'\r\n':
                 break
 
@@ -1137,5 +1153,10 @@
         self.args = line,
         self.line = line
 
+class LineTooLong(HTTPException):
+    def __init__(self, line_type):
+        HTTPException.__init__(self, "got more than %d bytes when reading %s"
+                                     % (_MAXLINE, line_type))
+
 # for backwards compatibility
 error = HTTPException
diff --git a/Lib/http/server.py b/Lib/http/server.py
index f1538f4..515572f 100644
--- a/Lib/http/server.py
+++ b/Lib/http/server.py
@@ -314,8 +314,12 @@
         self.command, self.path, self.request_version = command, path, version
 
         # Examine the headers and look for a Connection directive.
-        self.headers = http.client.parse_headers(self.rfile,
-                                                 _class=self.MessageClass)
+        try:
+            self.headers = http.client.parse_headers(self.rfile,
+                                                     _class=self.MessageClass)
+        except http.client.LineTooLong:
+            self.send_error(400, "Line too long")
+            return False
 
         conntype = self.headers.get('Connection', "")
         if conntype.lower() == 'close':
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):