In this paper we construct a two-country search model to determine the nominal exchange rate between two fiat monies. Our model allows agents to use any currency to trade for goods in all countries. However, search frictions restrict agents opportunities for instantaneous arbitrage, and hence make the nominal exchange rate determinate. The nominal exchange rate depends on the two countries economic fundamentals, including the stocks and growth rates of the two monies. Direct exchanges between currencies are essential and they imply a nominal exchange rate that is different from the relative price between the two currencies in the goods markets. There are persistent violations of the law of one price and purchasing power parity in equilibrium, despite the fact that prices are perfectly flexible and all goods are tradeable between countries. Nominal and real exchange rates can move together in the steady state in response to money growth shocks.Exchange Rates; Search; Money; Currency Trade.