In an ATM cell multiplexer which multiplexes ATM cells outputted from a plurality of cards, sequential cell arrival numbers common to the ATM cells outputted from a plurality of cards are added to each of the cells to be written in memories, and the read side checks a sequentiality of the cell arrival numbers whereby the ATM cells are read in the order of arrival and the cell arrival number at that time is used as the cell arrival number to be checked at the next read time. Also, when any of the cards is pulled out, a card not pulled out is operated normally and an address counter of only the pulled-out card is cleared. Even when non-sequentiality of the cell arrival numbers occurs due to the clearance of the address counter, the maximum cell arrival number is set to the value which enables the oldest cells to be read first. Furthermore, by the division of storing memories according to priority degrees, a read control identifying the ATM cells for a real time system as well as the ATM cells for a data system can be performed.