diff --git a/Lib/xmlrpc/server.py b/Lib/xmlrpc/server.py
index aef2eb2..04820bf 100644
--- a/Lib/xmlrpc/server.py
+++ b/Lib/xmlrpc/server.py
@@ -469,7 +469,9 @@
             if hasattr(self.server, '_send_traceback_header') and \
                     self.server._send_traceback_header:
                 self.send_header("X-exception", str(e))
-                self.send_header("X-traceback", traceback.format_exc())
+                trace = traceback.format_exc()
+                trace = str(trace.encode('ASCII', 'backslashreplace'), 'ASCII')
+                self.send_header("X-traceback", trace)
 
             self.end_headers()
         else:
diff --git a/Misc/NEWS b/Misc/NEWS
index 1a6d17a..1ed921c 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -28,6 +28,9 @@
 Library
 -------
 
+- Issue #7606: XML-RPC traceback stored in X-traceback is now encoded to ASCII
+  using backslashreplace error handler
+
 - Issue #5277: Fix quote counting when parsing RFC 2231 encoded parameters.
 
 - Issue #8383: pickle and pickletools use surrogatepass error handler when