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Peer-to-peer (P2P) video-on-demand (VoD) is a popular Internet service for a large number of concurrent users. Streaming capacity in a P2P VoD system is defined as the maximum streaming rate that can be received by every user. In this letter, we study the streaming capacity problem in P2P VoD systems. We formulate the streaming capacity problem into an optimization problem which maximizes the streaming rate subject to peer bandwidth constraints, and then solve it with a distributed algorithm. From the study on streaming capacity, we find that the streaming capacity is limited by the over-demanded video segments. Therefore we introduce helpers, the peers who are willing to contribute their remaining upload bandwidths to help other peers, into P2P VoD systems. We optimize helper assignment and rate allocation to improve the streaming capacity. In the simulations, we demonstrate that the streaming capacity can be obtained in a distributed manner by optimizing the resource allocation in the P2P VoD system.