We present a detailed dielectric study of the relaxation effects that occur in several perovskite rare-earth manganites, including the multiferroics TbMnO(3) and DyMnO(3). We demonstrate that the strong magnetocapacitive effects, observed for electrical fields E parallel c, are nearly completely governed by magnetic-state induced changes of the relaxation parameters. The multiferroic materials, which undergo a transition into a spiral magnetic state, show qualitatively different relaxation behavior than those compounds transferring into an A-type antiferromagnetic state. We ascribe the relaxations in both cases to the off-center motion of the manganese ions, which in the multiferroic systems also leads to the ferroelectric ordering.