We study fairness of resource allocation in multirate, multicast networks. In multirate networks, different receivers of the same multicast session can receive service at different rates. We develop a mathematical framework to model the maxmin fair allocation of bandwidth with minimum and maximum rate constraints. We present a necessary and sufficient condition for a rate allocation to be maxmin fair in a multirate, multicast network. We propose a distributed algorithm for computing the maxmin fair rates allocated to various source–destination pairs. This algorithm has a low message exchange overhead, and is guaranteed to converge to the maxmin fair rates in finite time.