In this paper, we investigate equilibrium cycles in dynamic general equilibrium models with cash-in-advance constraints. Our findings are two-fold. First, in such models, if an equilibrium cycle exists, then there also exists a continuum of equilibrium cycles in its neighborhood. Second, the limit cycle, to which a dynamic path converges, varies continuously according to the initial distribution of the money holdings. Thus, temporary shocks that affect the initial distribution have permanent effects in such models; that is, such models exhibit hysteresis. Furthermore, we also explore the logic behind the results.