The service model of Erlang with n servers, Poisson input, and exponential distributed service times isgeneralized in such a way that one can consider service times which can be dependent and have arbitary distributions. A sufficient condition is given for the existence of a uniquely determined stationary distribution for the state of the system. As in the case of the usual Erlang model, this distribution can be described by the well known Erlang formulas. The condition requires that the service times of different servers form stationary series which are independent of each other.