Customer loyalty as part of user behaviour has significant impact on the Internet Service Providers' (ISPs) price setting strategies as shown recently in [1,2,3,4]. However, the issue of a dynamic ISP market, where new ISPs enter the market and try to increase their market shares by offering favourable access prices for incumbent ISPs' loyal customers, has not been addressed yet. Furthermore, the cost of entrance is not yet properly dealt with in the previous studies. In this paper, we use the tools from game theory to understand the competition for market share in a dynamic ISP market with customer loyalty. We model the situation by a Stackelberg leader-follower game, and use the model to compute the Nash/Stackelberg equilibria of the game with customer loyalty and different cost models. For simple cost models, we give explicit formulas for the equilibria of the games. For more complex cost models, we use approximation and simulations to illustrate the dynamics of market shares in these situations. ́ Springer-Verlag Berlin Heidelberg 2009.