The need for understanding of various real-life queueing situations has caused the theory of queues to grow in various directions. One of these directions treats the class of systems where more than one service is available to, or required by, each customer, The theory for this class has progressed along a central path from which various developments branch. Multichannel poisson queues constitute the first part of the path; series and then networks of poisson stations follow. The branches from the path involve models with non-poisson or general assumptions, models with limited waiting room or limited numbers of customers, models with nonzero transit times, and others. The path leads to models for communication networks, and hence to models for computer networks. The theory of computer timesharing branches from the beginning of the path. The dissertation attempts to outline the present state of the theory for those models which occur on this path or its branches. The derivation of probability distributions for queue length and waiting time are presented in full for models on the central path, and in brief for the other models.