A model of monetary exchange with private financial intermediation is constructed. Claims on financial intermedaries of two types are traded in transactions: circulating notes and deposits. There can be a role for the government in supplying liqudity, and level changes in the money supply accomplished through open market operations can be nonneutral. A Friedman rule is suboptimal, due to costs of maintaining the stock of currency. The model is used to address some issues related to current monetary policy in the United States.