To support the requirements for the transmission of continuous media, such as audio and video, multiservice packet-switching networks must provide service guarantees to connections, including guarantees on throughput, network delays, and network delay variations. For the most demanding applications, the network must offer a service which provides deterministically bounded delay guarantees, referred to as ''bounded delay service.'' The admission control functions in a network with a bounded delay service require 'schedulability conditions' that detect violations of delay guarantees in a network switch, In this paper, exact schedulability conditions are presented for three packet scheduling methods: earliest-deadline-first (EDF), static-priority (SP), and a novel scheduling method, referred to as rotating-priority-queues (RPQ), By characterizing the worst-case traffic with general subadditive functions, the presented schedulability conditions can be applied to a large class of traffic models, Examples, which include actual MPEG video traces, are presented to demonstrate the trade-offs involved in selecting a packet scheduling method for a bounded delay service.