[en] It was shown in a previous paper that kickers with a high repetition rate can be designed by combining several cavities operating in a deflecting mode. In this paper we simplify this idea by showing that such kickers can be built also with one cavity or with an assembly of coupled cavities operating at several frequencies. We also demonstrate that this concept can be used for accelerating cavities. The electrical breakdown limit for such multimode accelerating cavities will be significantly higher than conventional single-mode cavities; therefore higher acceleration gradients, e.g., for linear colliders, can be achieved. 2 refs., 4 figs