2002 Buick Century fuel gage problem

I have a 2002 buick century with 130kmiles on it. Something wierd is happening with the fuel gage. When I start the engine it might jump to full and a few seconds later go to zero and go up and down slowly in a jerky fashion, usually ending at about where it should be. For instance if the tank is half full it will sort of end at half full but jerk a little from time to time up or down a little bit. One thing I noticed when I go to start the engine -before I start it when I turn the key to the run postion with the starter not yet engaged, the gage goes up to the correct position in a jerky motion. What might be wrong?