Abstract: A queuing model with two sequential servers is developed to analyze performance in computer and communication systems. In one case the CPU is the first server and the terminal and its associated communications equipment are the second server. In a second case the CPU and the channel are the first server and the auxiliary storage device is the second server. We study the queuing behavior of the sequential server systems with Poisson arrivals, general service time distributions, and several service disciplines, including bulk arrivals, message priorities, and the input and output queues. The stationary distributions of the queue lengths and waiting times are determined by using an imbedded Markov chain analysis. Several examples are given to illustrate the applications of these models to practical problems.