The fuel pump on my 95 Riviera keeps on running for quite a while after I have turned the ignition off. Does this mean that I am losing fuel pressure and/or does it mean that the pump will need replacing? Any other suggestions?

Britman,
Your fuel pump relay is likely sticking on. This will drain your battery if it remains on too long after the engine is shut off. It is a pretty simple repair.
Tim

Hi Tim,

Thank you so much for the help. You are right, my battery does keep running low! I haven't looked yet, but my guess is that the relay is under the back seat. The contacts have probably welded together. All I have to do is change the relay, (not worth filing the contacts on a 13 yr old relay). That is a big relief, much better than having to pull out the tank and replace the fuel pump. Have a great day Tim.

Chris.