diff --git a/rest_framework/request.py b/rest_framework/request.py
index 7e4daf2749..5cd1ceaa88 100644
--- a/rest_framework/request.py
+++ b/rest_framework/request.py
@@ -153,6 +153,12 @@ class Request(object):
 
     def __init__(self, request, parsers=None, authenticators=None,
                  negotiator=None, parser_context=None):
+        # If we're being passed our own Request object, unwrap the underlying
+        # HttpRequest. This allows for some backwards compatibilty to 3.7.3
+        # for select users who carefully reuse ViewSets.
+        if isinstance(request, Request):
+            request = request._request
+
         assert isinstance(request, HttpRequest), (
             'The `request` argument must be an instance of '
             '`django.http.HttpRequest`, not `{}.{}`.'
diff --git a/tests/test_request.py b/tests/test_request.py
index 76589a4401..6071e58772 100644
--- a/tests/test_request.py
+++ b/tests/test_request.py
@@ -33,10 +33,13 @@ def test_request_type(self):
 
         message = (
             'The `request` argument must be an instance of '
-            '`django.http.HttpRequest`, not `rest_framework.request.Request`.'
+            '`django.http.HttpRequest`, not `NoneType`.'
         )
         with self.assertRaisesMessage(AssertionError, message):
-            Request(request)
+            Request(None)
+
+        other_request = Request(request)
+        assert other_request._request is request._request
 
 
 class PlainTextParser(BaseParser):