A flow control procedure is presented for virtual circuit computer networks with multimedia data traffic. It is assumed that the data packets belong to different priority groups. Power is used as the performance measure for a virtual circuit (VC). The input rate controller of every virtual circuit selects a throughput which maximizes its own objective function. A distributed algorithm is given which can be executed by the input rate controllers of the VC's without the global knowledge of the network. It is shown that the algorithm coverages to the optimum of the objective function of every virtual circuit and the solution is shown to be independent of the initial throughputs. Some network examples are solved by analytical and numerical methods.>