A congestion control system for packet communications networks in which access to the network is controlled to prevent such congestion. Packets within the pre-specified statistical description of each packet source are marked as high priority ("green" packets) while packets exceeding the pre-specified characteristics are marked with a lower priority ("red" packets). The overall red packet rate is limited to prevent red packet saturation of the network. The introduction of red packets into the network is subjected to a degree of hysteresis to provide better interaction with higher layer error recovery protocols. The amount of hysteresis introduced into the red packet marking can be fixed or varied, depending on the statistics of the incoming data packets at the entry point to the network.