In an ATM switching system, bi-directionally coupling devices establish connections between corresponding interface units and an ATM switching module. The switching module includes a self-routing switch, an input distribution network for establishing connections between the bi-directionally coupling devices and the input ports of the self-routing switch, and an output distribution network for establishing connections between the output ports of the self-routing switch and bi-directionally coupling devices. The bi-directionally coupling devices and the input and output distribution networks are controlled in accordance with data supplied from the interface units indicating the directions of signals passing through the interface units and the operating speed of the interface units.