In multipoint-to-point connections, the tra c at the root destination is the combination of all tra c originating at the leaves. A crucial concern in the case of multiple senders is how to de ne fairness within a multicast group, and among groups and point-to-point connections. Fairness de nition can be complicated since the multipoint connection can have the same identi er VPI VCI on each link, and senders might not be distinguishable in this case. Many rate allocation algorithms implicitly assume that there is only one sender in each VC, which does not hold for multipoint-to-point cases. We give v arious possibilities for de ning fairness for multipoint connections, and show the tradeo s involved. In addition, we show that ATM bandwidth allocation algorithms need to be adapted to give fair allocations for multipoint-to-point connections.