We analyze an M I , M2/G1,G2/1/N queue with different scheduling and push-out scheme in this paper. Our work is motivated by the study of the performance of an output link of ATM switches with two-class priority traffics. The queueing model developed in this paper is more general than that of the output link of ATM switches with two-class priority traffics. We can have general service time distributions for classes 1 and 2, and a general service discipline function, al(z,j), with a l ( i , j ) being the probability that a class 1 packet will be served, given that there are i class 1 and j class 2 packets waiting for service. We obtain an exact solution for loss probabilities for classes 1 and 2, the queue length distribution and the mean waiting time for class 1 and an approximate calculation for the queue length distribution and mean waiting time for class 2. We show that our approximation is an upper bound and the error due to the approximation is very small when the loss probability of class 2 is small (e.g., 5 0.01).