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The main purpose of many current peer-to-peer (P2P) networks is off-line file sharing. However, a potentially very promising use of such networks is to share video streams (e.g., TV programs) in real time. In order to do so, the peers in a P2P network who are interested in the same video stream may employ Application Level Multicasting (ALM). In existing P2P networks, peers may exhibit behavior which is problematic for ALM: they are not always willing to donate resources (free-riding), and they may arrive and depart at a high rate (churn). In this paper we propose the Orchard algorithm for creating and maintaining ALM trees in P2P networks, which deals with both these problems. By employing a technique called Multiple Description Coding, we split a video stream into several substreams. Orchard creates a dynamic spanning tree for each of these substreams in such a way that in the resulting forest, no peer has to forward more substreams than it receives. Based on an analysis of the expected performance of Orchard and on experiments in a real system, we find that Orchard is capable of maintaining a multicast forest, even when peers join and leave the forest at a high rate.