diff --git a/Lib/email/FeedParser.py b/Lib/email/FeedParser.py
index ac3769d..af0e177 100644
--- a/Lib/email/FeedParser.py
+++ b/Lib/email/FeedParser.py
@@ -314,6 +314,9 @@
                     # body parts within such double boundaries.
                     while True:
                         line = self._input.readline()
+                        if line is NeedMoreData:
+                            yield NeedMoreData
+                            continue
                         mo = boundaryre.match(line)
                         if not mo:
                             self._input.unreadline(line)