This paper analyzes a two-good version of the Diamond and Dybvig model in a small open economy. This structure is used to analyze the interaction between banks as liquidity insurers, real exchange rates and monetary policies. It is shown that fixed exchange rates with a Central Bank providing liquidity in pesos implements the efficient allocation. The conditions for a run equilibrium in this system are stronger than in the literature. In a flexible exchange rate regime, multiple equilibria cannot be eliminated. In particular, there is an equilibrium where a fraction of patient consumers purchases dollars in the interim period. This can be interpreted as a partial currency run event. A dollarized banking system may also implement the efficient allocation under some conditions.