The paper studies routing in loss networks in the framework of a non-cooperati- ve game with selfish users. Two solution concepts are considered: the Nash equilibrium, corresponding to the case of a finite number of agents (such as service providers) that take routing decisions, and the Wardrop equilibrium, in which routing decisions are taken by a very large number of individual users. We show that these equilibria do not fall into the standard frameworks of non-cooperative routing games. As a result, we show that uniqueness of equilibria or even of utilizations at equilibria may fail even in the case of simple topology of parallel links. However, we show that some of the problems disappear in the case in which the bandwidth required by of all connections is the same. For the special case of a parallel link topology, we obtain some surprisingly simple way of solving the equilibrium for both cases of Wardrop as well as Nash equilibrium.