The paper presents exact schedulability analyses for real-time systems scheduled at run-time with a static priority pre-emptive dispatcher. The tasks to be scheduled are allowed to experience internal blocking (from other tasks with which they share resources) and (with certain restrictions) release jitter — such as waiting for a message to arrive. The analysis presented is more general than that previously published, and subsumes, for example, techniques based on the Rate Monotonic approach. In addition to presenting the theory, an existing avionics case study is described and analysed. The predictions that follow from this analysis are seen to be in close agreement with the behaviour exhibited during simulation studies. 1.