This paper develops a model to investigate the mechanisms of acceptability of private money. During the 1990s, in Russia, the official money lose ground to privately created means of payment whose share in inter-firm transactions increased rapidly in the period between 1995-1998. Considering that the acceptability of private means of payment in certain circumstances can become self-reinforcing, we argue that the demonetization in Russia has been a result of the driving forces of a particular equilibrium. To explore the mechanism of acceptability of private money, we propose a simple model based on the matching process which partitions all agents in physically and informationally separate groups in each moment in time. We show that the use of endogenous money is always a possible trade pattern