—This article studies the scheduling of critical embedded systems, which consist of a set of communicating periodic tasks with constrained deadlines. Currently, tasks are usually sequenced manually, partly because available scheduling policies do not ensure the determinism of task communications. Ensuring this determinism requires scheduling policies supporting task precedence constraints (which we call dependent tasks), which are used to force the order in which communicating tasks execute. We propose fixed priority scheduling policies for different classes of dependent tasks: with simultaneous or arbitrary release times, with simple precedences (between tasks of the same period) or extended precedences (between tasks of different periods). We only consider policies that do not require synchronization mechanisms (like semaphores). This completely prevents deadlocks or scheduling anomalies without requiring further proofs.