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We present an admission control scheme which provides per-flow delay and bandwidth guarantees based solely upon simple class-based strict priority queueing. We derive basic properties of the worst-case behaviour in strict priority queueing systems using network calculus. Building upon these properties, a flow admission control scheme is devised. The rationale behind this work is the appealing simplicity as well as the almost ubiquitous availability of strict priority queueing in today's routers and the thus promising applicability of our results for practical purposes in providing quality of service (QoS) in the Internet.