A number of repairman-type models useful for describing and evaluating time-sharing computer systems with multitype users are presented and analyzed. Several approximation methods are introduced including one which allows for performance evaluation as a function of the queue discipline. Diffusion approximations are also considered, the accuracy of each of the approximation methods is assessed by numerical methods. The models proposed should prove to be useful for planning and evaluating both new and existing time-sharing computer systems. (Author)