—Most theoretical research on routing games in telecommunication networks has so far dealt with reciprocal congestion effects between routed entities. Yet in networks that support differentiation between flows, the congestion experienced by a packet depends on its priority level. Another differentiation is made by compressing the packets in the low priority flow while leaving the high priority flow intact. In this paper we study such kind of routing scenarios for the case of non-atomic users and we establish conditions for the existence and uniqueness of equilibrium.