A congestion control system appropriately controls congestion of cells independently of the configuration of source and destination terminal units in, for example, an ATM switching unit, and shortens the time taken from the generation of congestion to the start of control. A buffer for switching the cells in a switch device adds to the cells transmitted through the switch device an EFCI for use in notifying the destination terminal unit of the congestion state of the cells. An output line device detects together with a VPI/VCI the EFCI added to the cell to be output from the switch device to the destination terminal unit. The output line device transmits to the switch device the VPI/VCI corresponding to the detected EFCI and an RM cell in which backward congestion indication is set.