Fisher's runaway process of sexual selection is potentially an important force generating character divergence between closely related populations. We investigated the evolution of multiple female preferences by Fisher's runaway process. There are two outcomes of runaway. The first is the evolution of mate preference to a stable equilibrium. This evolution occurs if the benefits of mate choice are sufficiently large relative to the cost of choice. Alternatively, mate preferences evolve cyclically. The rate and pattern of cyclic evolution depends primarily on the individual cost of choice and epistasis in the joint cost of choice. If there are small differences in natural selection (e.g., predation risk) between populations, cyclic evolution quickly leads to divergence in mate preferences and sexual ornaments and so to sexual isolation.