International audienceThe real-time system design targeting multiprocessor platforms leads to two important complications in real-time scheduling. First, to ensure deterministic processing by communicating tasks the scheduling has to consider precedence constraints. The second complication factor is mixed criticality, i.e., integration upon a single platform of various subsystems where some are safety-critical (e.g., car braking system) and the others are not (e.g., car digital radio). Therefore we motivate and study the multiprocessor scheduling problem of a finite set of precedence-related mixed criticality jobs. This problem, to our knowledge, has never been studied if not under very specific assumptions. The main contribution of our wor...