Momentary equilibria are defined as points that satisfy agents’ optimality conditions and market clearing at any date. However, some dynamic sequences commencing from such points may not be considered valid equilibria because they asymptotically violate some economic restriction of the model. This paper studies a pure-exchange monetary overlapping generations economy in which young and old agents face exogenous minimum consumption requirements, and money is the only asset. The presence of the minimum consumption requirement on the old is shown to produce multiperiodic monetary equilibria in which real balances cycle forever between “momentary” equilibrium points (those which generate monetary sequences that potentially violate equilibrium strictures asymptotically). The novelty is to show that segments of the intergenerational offer curve that would have been deemed dynamically invalid can, in fact, be used to produce asymptotically valid cyclical paths. Indeed, a limit cycle can bestow dynamic validity on momentary equilibrium points that had erstwhile been classified as dynamically invalid.