I have almost the exact same bike as you, a 99 S3 with 34k miles ('bout 75km) on the clock. I get a bit of backfiring when I let off on the throttle.
Does yours sound like it's sucking a little wind? If it is it may be an exhaust leak.
My old cr250 did the surge and die thing once too. Found out my step brother had done me the glorious favor of washing out the gas tank. Next time I put gas in it there was water in the tank, wreaked havoc with it. Did almost exactly what yours is doing. On my CR I just drained the tank and lines and added some fuel injector cleaner (supposed to get rid of water) even though the bike was carbuerated. Might wanna research that first, though. Check with cheapbastard, he'd know. Look in any of the other threads and you'll find him. At the bottom of one of his comment there's a tab where you can send him a private message.
Good luck and welcome to the asylum...

">
[ This message was edited by: Calitriple on 2006-07-14 03:30 ]