The objective of this paper is to study the stationary monetary equilibria of a stochastic overlapping generations model with a general incomplete asset structure. It is proved that a stationary equilibrium with a nonzero price of money generically exists and is locally isolated when there is outside money; for an open set of economies there is an equilibrium with positive money prices in all states. The equilibrium is also given a neat characterisation in terms of the properties of the underlying state prices. With only inside money there will instead be a continuum of equilibria.Journal of Economic LiteratureClassification Numbers: D52, D90, E40.