An ATM cell multiplexer is arranged so that in the up direction from the terminal equipments/ATM cell interfaces to the ATM switchboard the ATM bus scheduler allocates the transmission rights for each CLAD unit in accordance with a preset schedule table and predetermined service categories or traffic control for the transmission of cells, and in the down direction from the ATM switchboard to the terminal equipments/ATM cell interfaces the cells are broadcast to all of the CLAD units which decide for the reception of the cells as to whether or not the cells are addressed to themselves.