The competition between a central securities depository (CSD) and a custodian bank is analysed in a Stackelberg model. The CSD sets its prices first, the custodian bank follows. There are many investor banks each of which has to decide whether to use the service of the CSD or of the custodian bank. This decision depends on the prices and the investor bank's preferences for the inhomogeneous services of the two service providers. Since the custodian bank uses services provided by the CSD as input, the CSD can raise its rival's costs. However, due to network externalities, the CSD's equilibrium market share is not necessarily higher than socially optimal. This result has important policy implications that are related to a discussion currently taking place in the securities settlement industry.