Yes, it does. However, in order for two observers who had the same time initially to come back together and compare times (without having to make perspective-dependent corrections for how long light takes to get from one to the other), at least one of them must accelerate. Unlike the effects of relative velocity, the acceleration effects are not symmetrical. At the end, they both agree on which (or neither) aged more.
Mike W.
(published on 09/03/2008)