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We consider the problem of distributed packet selection and scheduling for multiple video streams sharing a communication channel. An optimization framework is proposed, which enables the multiple senders to coordinate their packet transmission schedules, such that the average quality over all video clients is maximized. The framework relies on rate-distortion information that is used to characterize a video packet. This information consists of two quantities: the size of the packet in bits, and its importance for the reconstruction quality of the corresponding stream. A distributed streaming strategy then allows for trading off rate and distortion, not only within a single video stream, but also across different streams. Each of the senders allocates to its own video packets a share of the available bandwidth on the channel in proportion to their importance. We evaluate the performance of the distributed packet scheduling algorithm for two canonical problems in streaming media, namely adaptation to available bandwidth and adaptation to packet loss through prioritized packet retransmissions. Simulation results demonstrate that, for the difficult case of scheduling nonscalably encoded video streams, our framework is very efficient in terms of video quality, both over all streams jointly and also over the individual videos. Compared to a conventional streaming system that does not consider the relative importance of the video packets, the gains in performance range up to 6 dB for the scenario of bandwidth adaptation, and even up to 10 dB for the scenario of random packet loss adaptation.