We consider the problem of channel sharing by rate adaptive streams belonging to various classes. The performance measure per class is the average scaled bandwidth allocated to connections in the class. We …rst provide a bandwidth adaptation policy that maximizes a linear combination of class performance measures; then, we use this result to characterize the region where the class performance measures lies under any bandwidth adaptation policy. Finally, based on the results above we use stochastic approximation techniques to provide a policy that optimizes a combination of concave rewards associated with class performance measures.