It is a known fact that the use of foreign currency by domestic residents shows significance persistence, even hysteresis. Temporary changes in the inflation rate can have permanent effects on the degree of currency substitution, as illustrated by the case of Bolivia, where dollarization has remained at a particularly high level after stabilization. The paper presents a simple model of currency substitution with network effects among agents with heterogeneous transaction costs. A network of foreign currency users reduces transactions costs for all prospective users of this currency. The strength of the network effects increases with size, which is defined as the number of agents whose foreign currency balances are larger than a given threshold. The network's size is endogenously determined. Its dynamics and the possibility of multiple equilibria generate patterns of currency substitution which exhibit persistence and hysteresis.