This paper develops a dynamic general equilibrium model with two currencies to study the effect of negative interest rates on domestic money demand and exchange rates. Money demand for a currency depends on the relative ratio of the money market rate and the deposit rate of the central bank. If agents choose to hold only domestic currency, a decrease in the deposit rate of the central bank will not affect the exchange rate. If agents choose to hold both currencies, a decrease in the deposit rate will cause an appreciation (depreciation) if the money market rate decreases to a larger (smaller) extent. If agents are subject to bank deposit rates that are sticky below zero, then a decrease of the central bank deposit rate leads to a depreciation of the currency regardless of the size of the effect on the money market rate.