diff --git a/Lib/doctest.py b/Lib/doctest.py
index dcbcfe5..ee71984 100644
--- a/Lib/doctest.py
+++ b/Lib/doctest.py
@@ -211,6 +211,13 @@
     else:
         raise TypeError("Expected a module, string, or None")
 
+def _newline_convert(data):
+    # We have two cases to cover and we need to make sure we do
+    # them in the right order
+    for newline in ('\r\n', '\r'):
+        data = data.replace(newline, '\n')
+    return data
+
 def _load_testfile(filename, package, module_relative, encoding):
     if module_relative:
         package = _normalize_module(package, 3)
@@ -221,7 +228,7 @@
                 file_contents = file_contents.decode(encoding)
                 # get_data() opens files as 'rb', so one must do the equivalent
                 # conversion as universal newlines would do.
-                return file_contents.replace(os.linesep, '\n'), filename
+                return _newline_convert(file_contents), filename
     with open(filename, encoding=encoding) as f:
         return f.read(), filename