ATM (Asynchronous Transfer Mode) has a fixed-length packet transport scheme. It is one of the promising proposals in B-ISDN.Since the packet length is fixed, it can be potentially to perform the various service to users. In this paper, a queueing model for an ATM multip`exer loaded by CBR and ON/OFF input sources is considered, and the two-queue system which each type of input sources has a queue with a finite capacity is analyzed. The cell loss probabilities for a performance measures of ATM multiplexer are derived, and are also evaluated through numerical examples. As a result, the cell loss probability of ON/OFF sources for the queue size is rapidly decreased when the multiplexed number and burstiness are increased. Since cells of the CBR source have lower priority than cells of the ON/OFF source, cell loss probabilities of CBR sources are accordingly high independently of CBR cell arrival rate when the number of CBR sources is large.