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Given that the Internet does not widely support Internet protocol multicast while content-distribution-network technologies are costly, the concept of peer-to-peer could be a promising start for enabling large-scale streaming systems. In our so-called Zigzag approach, we propose a method for clustering peers into a hierarchy called the administrative organization for easy management, and a method for building the multicast tree atop this hierarchy for efficient content transmission. In Zigzag, the multicast tree has a height logarithmic with the number of clients, and a node degree bounded by a constant. This helps reduce the number of processing hops on the delivery path to a client while avoiding network bottlenecks. Consequently, the end-to-end delay is kept small. Although one could build a tree satisfying such properties easily, an efficient control protocol between the nodes must be in place to maintain the tree under the effects of network dynamics. Zigzag handles such situations gracefully, requiring a constant amortized worst-case control overhead. Especially, failure recovery is done regionally with impact on, at most, a constant number of existing clients and with mostly no burden on the server.