diff --git a/Lib/tarfile.py b/Lib/tarfile.py
index 45997cb..87b298e 100644
--- a/Lib/tarfile.py
+++ b/Lib/tarfile.py
@@ -1065,7 +1065,8 @@
         self.closed = False
         self.members = []       # list of members as TarInfo objects
         self._loaded = False    # flag if all members have been read
-        self.offset = 0L        # current position in the archive file
+        self.offset = self.fileobj.tell()
+                                # current position in the archive file
         self.inodes = {}        # dictionary caching the inodes of
                                 # archive members already added
 
diff --git a/Lib/test/test_tarfile.py b/Lib/test/test_tarfile.py
index 5a50996..f3c090d 100644
--- a/Lib/test/test_tarfile.py
+++ b/Lib/test/test_tarfile.py
@@ -260,6 +260,38 @@
         mode = self.mode + self.sep + "*"
         self.tar = tarfile.open(tarname(self.comp), mode)
 
+class ReadFileobjTest(BaseTest):
+
+    def test_fileobj_with_offset(self):
+        # Skip the first member and store values from the second member
+        # of the testtar.
+        self.tar.next()
+        t = self.tar.next()
+        name = t.name
+        offset = t.offset
+        data = self.tar.extractfile(t).read()
+        self.tar.close()
+
+        # Open the testtar and seek to the offset of the second member.
+        if self.comp == "gz":
+            _open = gzip.GzipFile
+        elif self.comp == "bz2":
+            _open = bz2.BZ2File
+        else:
+            _open = open
+        fobj = _open(tarname(self.comp), "rb")
+        fobj.seek(offset)
+
+        # Test if the tarfile starts with the second member.
+        self.tar = tarfile.open(tarname(self.comp), "r:", fileobj=fobj)
+        t = self.tar.next()
+        self.assertEqual(t.name, name)
+        # Read to the end of fileobj and test if seeking back to the
+        # beginning works.
+        self.tar.getmembers()
+        self.assertEqual(self.tar.extractfile(t).read(), data,
+                "seek back did not work")
+
 class WriteTest(BaseTest):
     mode = 'w'
 
@@ -624,6 +656,8 @@
     comp = "gz"
 class ReadStreamAsteriskTestGzip(ReadStreamAsteriskTest):
     comp = "gz"
+class ReadFileobjTestGzip(ReadFileobjTest):
+    comp = "gz"
 
 # Filemode test cases
 
@@ -680,6 +714,8 @@
         comp = "bz2"
     class ReadStreamAsteriskTestBzip2(ReadStreamAsteriskTest):
         comp = "bz2"
+    class ReadFileobjTestBzip2(ReadFileobjTest):
+        comp = "bz2"
 
 # If importing gzip failed, discard the Gzip TestCases.
 if not gzip:
@@ -713,6 +749,7 @@
         ReadDetectFileobjTest,
         ReadAsteriskTest,
         ReadStreamAsteriskTest,
+        ReadFileobjTest,
         WriteTest,
         Write100Test,
         WriteSize0Test,
@@ -730,7 +767,8 @@
             ReadTestGzip, ReadStreamTestGzip,
             WriteTestGzip, WriteStreamTestGzip,
             ReadDetectTestGzip, ReadDetectFileobjTestGzip,
-            ReadAsteriskTestGzip, ReadStreamAsteriskTestGzip
+            ReadAsteriskTestGzip, ReadStreamAsteriskTestGzip,
+            ReadFileobjTestGzip
         ])
 
     if bz2:
@@ -738,7 +776,8 @@
             ReadTestBzip2, ReadStreamTestBzip2,
             WriteTestBzip2, WriteStreamTestBzip2,
             ReadDetectTestBzip2, ReadDetectFileobjTestBzip2,
-            ReadAsteriskTestBzip2, ReadStreamAsteriskTestBzip2
+            ReadAsteriskTestBzip2, ReadStreamAsteriskTestBzip2,
+            ReadFileobjTestBzip2
         ])
     try:
         test_support.run_unittest(*tests)