An ATM multiplexing apparatus for selectively performing cell discard processing in the case of congestion, on the basis of a use state of the same connection formed by cells from the side of an ATM switching unit and subscribers without installing UPC units. The ATM multiplexing apparatus, which is connected to the ATM switching unit and plural subscribers though ATM communication lines, performs multiplex processing to ATM cells sent from the plural subscribers. The ATM multiplexing apparatus has a detection means for detecting a level of a congestion state corresponding to the ATM cells received from the subscribers and discard means for selectively discarding the ATM cells received from the subscribers on the basis of a communication state determined by the ATM cells received from the ATM switching unit, ATM cells received from the subscribers and a level value of a warning signal indicating the detected congestion state.