If they aren't cracked in the sidewall and still are flexible I guess don't be too worried. I can't say whether you should be worried at all though but you migth avoid bombing down hills at over 40mph and leaning into turns hard of that kind of crazyness.
Personally I rode the original tires that I got on a used schwinn le tour IV (from the last year they were built in chicago) and they rode well until I replaced them with something more modern with flat protection.