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The major challenges of designing multicast rate-control protocols for a combined wired/wireless network are the varying transmission characteristics (bandwidth, error, and propagation delay) of the wireless and wired media, and the different, possibly conflicting flow control requests from multiple receivers. To address these issues, in this paper we study multicasting rate-control ABR algorithms for a combined wired/wireless network with unreliable links and irregular network feedback. We propose a new ABR multicast extension algorithm that can readily extend any unicast ABR rate control scheme for multicast services. By formal analysis, we show that it is max-min fair, and that its maximum cell loss is less than or equal to that of an existing algorithm proposed by K.Y. Siu and H.Y. Tseng (1997). We also extend the definition of global feasibility to multicast flows, and propose a delayed-increase policy to ensure global feasibility. Both the waiting time of the delayed-increase policy, and the maximum cell loss in the absence of the policy are formally analyzed. The new algorithm requires a waiting time no longer than, and has a maximum cell loss less than or equal to, that of the existing algorithm. The significance of our approach is illustrated by the formal analysis, which allows us to design a new multicast extension algorithm that is max-min fair, results in a small cell-loss bound, and achieves global feasibility. The analytical method may also assist the design and analysis of other multicasting flow algorithms over ATM and wireless ATM, and other network protocols such as multicast IP and mobile IP.