diff --git a/Doc/library/pyexpat.rst b/Doc/library/pyexpat.rst
index 3d88d85..cb8ab65 100644
--- a/Doc/library/pyexpat.rst
+++ b/Doc/library/pyexpat.rst
@@ -100,6 +100,11 @@
       http://www.python.org/ns/ elem1
       elem2
 
+   Due to limitations in the ``Expat`` library used by :mod:`pyexpat`,
+   the :class:`xmlparser` instance returned can only be used to parse a single
+   XML document.  Call ``ParserCreate`` for each document to provide unique
+   parser instances.
+
 
 .. seealso::
 
@@ -119,7 +124,9 @@
 
    Parses the contents of the string *data*, calling the appropriate handler
    functions to process the parsed data.  *isfinal* must be true on the final call
-   to this method.  *data* can be the empty string at any time.
+   to this method; it allows the parsing of a single file in fragments,
+   not the submission of multiple files.
+   *data* can be the empty string at any time.
 
 
 .. method:: xmlparser.ParseFile(file)
diff --git a/Lib/test/test_pyexpat.py b/Lib/test/test_pyexpat.py
index 8ef3917..95a614b 100644
--- a/Lib/test/test_pyexpat.py
+++ b/Lib/test/test_pyexpat.py
@@ -236,6 +236,18 @@
         operations = out.out
         self._verify_parse_output(operations)
 
+    def test_parse_again(self):
+        parser = expat.ParserCreate()
+        file = BytesIO(data)
+        parser.ParseFile(file)
+        # Issue 6676: ensure a meaningful exception is raised when attempting
+        # to parse more than one XML document per xmlparser instance,
+        # a limitation of the Expat library.
+        with self.assertRaises(expat.error) as cm:
+            parser.ParseFile(file)
+        self.assertEqual(expat.ErrorString(cm.exception.code),
+                          expat.errors.XML_ERROR_FINISHED)
+
 class NamespaceSeparatorTest(unittest.TestCase):
     def test_legal(self):
         # Tests that make sure we get errors when the namespace_separator value
diff --git a/Misc/NEWS b/Misc/NEWS
index 10ddd9a..5240f69 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -89,6 +89,11 @@
 - Issue #20817: Fix inspect.getcallargs() to fail correctly if more
   than 3 arguments are missing. Patch by Jeremiah Lowin.
 
+- Issue #6676: Ensure a meaningful exception is raised when attempting
+  to parse more than one XML document per pyexpat xmlparser instance.
+  (Original patches by Hirokazu Yamamoto and Amaury Forgeot d'Arc, with
+  suggested wording by David Gutteridge)
+
 Documentation
 -------------
 
diff --git a/Modules/pyexpat.c b/Modules/pyexpat.c
index a71ecc5..97f2b56 100644
--- a/Modules/pyexpat.c
+++ b/Modules/pyexpat.c
@@ -908,7 +908,7 @@
         void *buf = XML_GetBuffer(self->itself, BUF_SIZE);
         if (buf == NULL) {
             Py_XDECREF(readmethod);
-            return PyErr_NoMemory();
+            return get_parse_result(self, 0);
         }
 
         bytes_read = readinst(buf, BUF_SIZE, readmethod);