diff --git a/PIL/FliImagePlugin.py b/PIL/FliImagePlugin.py
index df6a4eb8e..772140076 100644
--- a/PIL/FliImagePlugin.py
+++ b/PIL/FliImagePlugin.py
@@ -127,8 +127,14 @@ class FliImageFile(ImageFile.ImageFile):
             return
         if frame < self.__frame:
             self._seek(0)
+
+        last_frame = self.__frame
         for f in range(self.__frame + 1, frame + 1):
-            self._seek(f)
+            try:
+                self._seek(f)
+            except EOFError:
+                self.seek(last_frame)
+                raise EOFError("no more images in FLI file")
 
     def _seek(self, frame):
         if frame == 0:
diff --git a/PIL/GifImagePlugin.py b/PIL/GifImagePlugin.py
index bd974b651..35fb95164 100644
--- a/PIL/GifImagePlugin.py
+++ b/PIL/GifImagePlugin.py
@@ -107,8 +107,14 @@ class GifImageFile(ImageFile.ImageFile):
             return
         if frame < self.__frame:
             self._seek(0)
+
+        last_frame = self.__frame
         for f in range(self.__frame + 1, frame + 1):
-            self._seek(f)
+            try:
+                self._seek(f)
+            except EOFError:
+                self.seek(last_frame)
+                raise EOFError("no more images in GIF file")
 
     def _seek(self, frame):
 
@@ -241,7 +247,7 @@ class GifImageFile(ImageFile.ImageFile):
 
         if not self.tile:
             # self.__fp = None
-            raise EOFError("no more images in GIF file")
+            raise EOFError
 
         self.mode = "L"
         if self.palette:
diff --git a/Tests/test_file_dcx.py b/Tests/test_file_dcx.py
index 7d2ae32d8..d59a5a785 100644
--- a/Tests/test_file_dcx.py
+++ b/Tests/test_file_dcx.py
@@ -34,6 +34,18 @@ class TestFileDcx(PillowTestCase):
         im = Image.open(TEST_FILE)
         self.assertEqual(im.n_frames, 1)
 
+    def test_eoferror(self):
+        im = Image.open(TEST_FILE)
+
+        n_frames = im.n_frames
+        while True:
+            n_frames -= 1
+            try:
+                im.seek(n_frames)
+                break
+            except EOFError:
+                self.assertTrue(im.tell() < n_frames)
+
     def test_seek_too_far(self):
         # Arrange
         im = Image.open(TEST_FILE)
diff --git a/Tests/test_file_fli.py b/Tests/test_file_fli.py
index 04c2006c9..1b95f793f 100644
--- a/Tests/test_file_fli.py
+++ b/Tests/test_file_fli.py
@@ -20,7 +20,19 @@ class TestFileFli(PillowTestCase):
 
     def test_n_frames(self):
         im = Image.open(test_file)
-        self.assertEqual(im.n_frames, 2)
+        self.assertEqual(im.n_frames, 1)
+
+    def test_eoferror(self):
+        im = Image.open(test_file)
+
+        n_frames = im.n_frames
+        while True:
+            n_frames -= 1
+            try:
+                im.seek(n_frames)
+                break
+            except EOFError:
+                self.assertTrue(im.tell() < n_frames)
 
 
 if __name__ == '__main__':
diff --git a/Tests/test_file_gif.py b/Tests/test_file_gif.py
index b15d32097..a38c360c9 100644
--- a/Tests/test_file_gif.py
+++ b/Tests/test_file_gif.py
@@ -135,8 +135,23 @@ class TestFileGif(PillowTestCase):
             self.assertEqual(framecount, 5)
 
     def test_n_frames(self):
+        im = Image.open(TEST_GIF)
+        self.assertEqual(im.n_frames, 1)
+
         im = Image.open("Tests/images/iss634.gif")
-        self.assertEqual(im.n_frames, 43)
+        self.assertEqual(im.n_frames, 42)
+
+    def test_eoferror(self):
+        im = Image.open(TEST_GIF)
+
+        n_frames = im.n_frames
+        while True:
+            n_frames -= 1
+            try:
+                im.seek(n_frames)
+                break
+            except EOFError:
+                self.assertTrue(im.tell() < n_frames)
 
     def test_dispose_none(self):
         img = Image.open("Tests/images/dispose_none.gif")
diff --git a/Tests/test_file_im.py b/Tests/test_file_im.py
index 24e00b2f0..76bf250a0 100644
--- a/Tests/test_file_im.py
+++ b/Tests/test_file_im.py
@@ -19,6 +19,18 @@ class TestFileIm(PillowTestCase):
         im = Image.open(TEST_IM)
         self.assertEqual(im.n_frames, 1)
 
+    def test_eoferror(self):
+        im = Image.open(TEST_IM)
+
+        n_frames = im.n_frames
+        while True:
+            n_frames -= 1
+            try:
+                im.seek(n_frames)
+                break
+            except EOFError:
+                self.assertTrue(im.tell() < n_frames)
+
     def test_roundtrip(self):
         out = self.tempfile('temp.im')
         im = hopper()
diff --git a/Tests/test_file_mpo.py b/Tests/test_file_mpo.py
index 1a0ebc453..c5562097d 100644
--- a/Tests/test_file_mpo.py
+++ b/Tests/test_file_mpo.py
@@ -99,6 +99,18 @@ class TestFileMpo(PillowTestCase):
         im = Image.open("Tests/images/sugarshack.mpo")
         self.assertEqual(im.n_frames, 2)
 
+    def test_eoferror(self):
+        im = Image.open("Tests/images/sugarshack.mpo")
+
+        n_frames = im.n_frames
+        while True:
+            n_frames -= 1
+            try:
+                im.seek(n_frames)
+                break
+            except EOFError:
+                self.assertTrue(im.tell() < n_frames)
+
     def test_image_grab(self):
         for test_file in test_files:
             im = Image.open(test_file)
diff --git a/Tests/test_file_psd.py b/Tests/test_file_psd.py
index dca3601b2..ea3856fce 100644
--- a/Tests/test_file_psd.py
+++ b/Tests/test_file_psd.py
@@ -23,6 +23,19 @@ class TestImagePsd(PillowTestCase):
         im = Image.open(test_file)
         self.assertEqual(im.n_frames, 2)
 
+    def test_eoferror(self):
+        im = Image.open(test_file)
+
+        n_frames = im.n_frames
+        while True:
+            n_frames -= 1
+            try:
+                # PSD seek index starts at 1 rather than 0
+                im.seek(n_frames+1)
+                break
+            except EOFError:
+                self.assertTrue(im.tell() < n_frames)
+
 
 if __name__ == '__main__':
     unittest.main()
diff --git a/Tests/test_file_tiff.py b/Tests/test_file_tiff.py
index 02a63586c..a88b49d7f 100644
--- a/Tests/test_file_tiff.py
+++ b/Tests/test_file_tiff.py
@@ -157,6 +157,18 @@ class TestFileTiff(PillowTestCase):
         im = Image.open('Tests/images/multipage.tiff')
         self.assertEqual(im.n_frames, 3)
 
+    def test_eoferror(self):
+        im = Image.open('Tests/images/multipage-lastframe.tif')
+
+        n_frames = im.n_frames
+        while True:
+            n_frames -= 1
+            try:
+                im.seek(n_frames)
+                break
+            except EOFError:
+                self.assertTrue(im.tell() < n_frames)
+
     def test_multipage(self):
         # issue #862
         im = Image.open('Tests/images/multipage.tiff')