Feels like shifting gears?
I've got a small problem with an '86 Schwinn Sprint that I picked up from craigslist: more often than not, when I'm pedaling up a hill or something like that, the bike feels and sounds as though it's suddenly shifting gears. It doesn't actually shift, though, since I don't notice a change in resistance.
Any ideas what the problem could be?
Sounds like the derailleur may need adjusted. Have you looked into doing this yet? It's easy to do, there's some videos on youtube explaining how to do this.
Good adjustment instructions can be found at www.parktool.com.