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In this paper we introduce an equation-based smooth multicast congestion control for adaptive multimedia transmission over best-effort wired networks. Target of the proposed schema is (a) smooth transmission rate, in order to minimize the audio-video (AV) encoding and decoding distortion and (b) TCP friendly transmission. The "smoothness" lays in the way the TCP-friendly transmission rate is filtered. We integrate the congestion control functions in the RTP protocol and use the RTCP sender and receiver reports to provide the necessary feedback information for the sender's adaptive transmission rate. The performance evaluation of the smooth adaptation and TCP-friendliness is conducted through a number of simulations with the network simulator software (ns2). Our intention is to use this congestion control in the context of a proposed framework for multimedia transmission over wired and wireless networks.