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We consider the problem of congestion control in networks which support both multirate multicast sessions and unicast sessions. We present a decentralized algorithm which enables the different rate-adaptive receivers in different multicast sessions to adjust their rates to satisfy some fairness criterion. A one-bit ECN marking strategy to be used at the nodes is also proposed. The congestion-control mechanism does not require any per-flow state information for unicast flows at the nodes. At junctions nodes of each multicast tree, some state information about the rates along the branches at the node may be required. The congestion-control mechanism takes into account the diverse user requirements when different receivers within a multicast session have different utility functions, but does not require the network to have any knowledge about the receiver utility functions.