Purposes of this paper are to study theoretically competition of international currencies, and to clarify a future situation of international monetary regime. For the purposes, after we make a clear synergy effects the functions of international currencies have, a dynamic model with decreasing cost function for international currencies competition is suggested to investigate stability of an international monetary regime.
  The implication from our model is that the larger an effect of network exterreality is, the more unstable international monetary regime is, by the reason of hard international currencies competition. For the sake of preventing such instability, monetary authorities should cooperate internationally on monetary policies and supervision.