We study how competition from privately supplied currency substitutes a¤ects monetary policy. We focus on regimes where monetary policy must be sequentially optimal. We obtain that the workings of competition between currency and currency substitutes depend critically on government objectives. However, the impact inside money competition has on equilibrium outcomes does not. In fact, we show that, in general, it enhances e¢ciency and reduces equilibrium in‡ation rates. Nevertheless, if the supply of “inside monies” is very e¢cient, then the equilibrium with currency may not be sustainable and only “inside money” will be held in equilibrium.