Every router in a network is provided with flow detecting means that detects a flow from a packet header of a packet so as to perform such packet processings as bandwidth monitoring, priority-based transferring, statistical information collecting with respect to each packet flow. Receiving a packet from a site, an edge router detects the packet flow and writes a flow identifier in the packet. Each flow identifier is uniquely decided in the network. The Internet router performs such packet processings as bandwidth monitoring, priority-based transferring, statistical information collecting with respect to each flow according to the flow identifier. The present invention can thus prevent the network from degradation of transferring performance caused by the flow detecting means of a backbone router.