Summary form only given, as follows. A neural network model for traffic controls in multistage interconnection networks is discussed. The goal of the neural network model is to find conflict-free traffic flows to be transmitted among given I/O traffic demands in order to maximize the network throughput. The model requires n2 processing elements for the traffic control in an n × n multistage interconnection network. The model runs not only on a sequential machine but also on a parallel machine with maximally n2 processors. The model was verified by solving ten 32 × 32 network problems.