What is the towing capacity of 1998 GMC 3500 quad cab diesel dually?

the max is 16,700 lbs

Yes, it depends which diesel you have in it and what kind of hitch/5th wheel setup you have but you are looking at 16,700 as a max as Ryan has suggested.

i know the question is a old one but,the factory towing spec is 8k for a 4wd dually crew with the 6.5 and auto trans, manual trans is 7k(6.5 not rated for 5th wheel) if it had a 454 then the bumper pull spec is 10k and 5th wheel is 10.5k with 4:10 and 12.5k with 4:56

Again i know this is lod but when you say bumper pull you actually mean the ball on the bumper or a trailering hitch and reciever??

centurionpackard, by bumper pull i mean by the factory class 5 hitch