We consider the existence of deterministically cycling steady state equilibria in a class of stationary overlapping generations models with sufficiently long (but, finite) lived agents. Preferences are of the discounted sum of utilities type with a fixed discount rate. Utility functions with large coefficients of relative risk aversion which generate strong income effects (relative to substitution effects) and backward bending offer curves are permitted. Lifetime endowment patterns are quite arbitrary. We show that if agents have a positive discount rate, then as agents1 lifespans get large, short period non-monetary cycles will disappear. Further, constant monetary steady states do not exist and therefore, neither do stationary monetary cycles of any period. We then consider the case where agents have a negative discount rate and show that there are robust examples in which constant monetary steady states as well as stationary monetary cycles (with undiminished amplitude) can occur no matter how long agents live.