A major challenge for the design of multiservice networks with Quality-of-Service guarantees is an efficient implementation of a bounded delay service, that is, a service that guarantees maximum end-to-end delays for every packet from a single traffic stream. A crucial component of a bounded delay service is the multiplexing method employed at network switches. On the one hand, to achieve a high network utilization, the multiplexing method should be highly sophisticated. On the other hand, since multiplexing is to be performed at the rate of the network links, the complexity of the multiplexing method should be strictly limited. We present a novel packet multiplexing technique, called Rotating Priority Queues (RPQ), that can support a bounded delay service to a large number of connections, yet maintains a low level of complexity. The operations required for RPQ multiplexing are similar to those of the simple, but inefficient, Static-Priority (SP) multiplexing method. The overhead of RPQ, as compared to SP, consists of a periodic rearrangement ("Rotation") of priority queues; the queue rotations are implemented by merely updating a set of pointers. It is shown that the network utilization achievable with RPQ multiplexing can be made arbitrarily close to the highly efficient, yet complex, Earliest-Deadline-Due (EDF) multiplexing method. We derive exact admission control tests for RPQ multiplexers and compare the utilization limits achievable with RPQ multiplexers to those of EDF and SP packet multiplexers.