Abstract: An asynchronous transfer mode (ATM) multiplexing process device and a method for processing a broadband integrated service digital network subscriber access apparatus. The device is equipped with input buffering means for storing the input cell momentarily, cell identification means classifying the input cell data per QOS class, QOS class buffering means storing the cells per class, scheduling control means controlling the scheduling order, scheduling means outputting the cells to the outside in the scheduling order and connection state management means connecting the network operator and the ATM multiplexing process device. The method includes a first step of determining if a buffer is full after classifying the cells, a second step of outputting the cells after granting priority if the buffer is full and a third step of outputting the cells in the class order if the buffer is not full.