diff -r 031fc0231f3d Lib/test/test_zipfile.py
--- a/Lib/test/test_zipfile.py	Thu Jan 15 22:53:21 2015 +0100
+++ b/Lib/test/test_zipfile.py	Fri Jan 16 21:30:08 2015 +0200
@@ -1668,6 +1668,34 @@ class LzmaTestsWithRandomBinaryFiles(Abs
     compression = zipfile.ZIP_LZMA
 
 
+# Privide the tell() method but not seek()
+class Tellable:
+    def __init__(self, fp):
+        self.fp = fp
+        self.offset = 0
+
+    def write(self, data):
+        self.offset += self.fp.write(data)
+
+    def tell(self):
+        return self.offset
+
+    def flush(self):
+        pass
+
+class UnseekableTests(unittest.TestCase):
+    def test_writestr_tellable(self):
+        f = io.BytesIO()
+        with zipfile.ZipFile(Tellable(f), 'w', zipfile.ZIP_STORED) as zipfp:
+            zipfp.writestr('ones', b'111')
+            zipfp.writestr('twos', b'222')
+        with zipfile.ZipFile(f, mode='r') as zipf:
+            with zipf.open('ones') as zopen:
+                self.assertEqual(zopen.read(), b'111')
+            with zipf.open('twos') as zopen:
+                self.assertEqual(zopen.read(), b'222')
+
+
 @requires_zlib
 class TestsWithMultipleOpens(unittest.TestCase):
     @classmethod
diff -r 031fc0231f3d Lib/zipfile.py
--- a/Lib/zipfile.py	Thu Jan 15 22:53:21 2015 +0100
+++ b/Lib/zipfile.py	Fri Jan 16 21:30:08 2015 +0200
@@ -1498,7 +1498,11 @@ class ZipFile:
                 "Attempt to write to ZIP archive that was already closed")
 
         zinfo.file_size = len(data)            # Uncompressed size
-        self.fp.seek(self.start_dir, 0)
+        try:
+            self.fp.seek(self.start_dir)
+        except (AttributeError, io.UnsupportedOperation):
+            # Some file-like objects can provide tell() but not seek()
+            pass
         zinfo.header_offset = self.fp.tell()    # Start of header data
         if compress_type is not None:
             zinfo.compress_type = compress_type
@@ -1543,7 +1547,11 @@ class ZipFile:
 
         try:
             if self.mode in ("w", "a") and self._didModify: # write ending records
-                self.fp.seek(self.start_dir, 0)
+                try:
+                    self.fp.seek(self.start_dir)
+                except (AttributeError, io.UnsupportedOperation):
+                    # Some file-like objects can provide tell() but not seek()
+                    pass
                 for zinfo in self.filelist:         # write central directory
                     dt = zinfo.date_time
                     dosdate = (dt[0] - 1980) << 9 | dt[1] << 5 | dt[2]