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In this paper we study the global scheduling of periodic task systems upon uniform multiprocessor platforms. We first show two very general properties which are well-known for uniprocessor platforms and which remain for multiprocessor one: (i) under few and not so restrictive assumptions, we show that any feasible schedules of periodic task system are periodic from some point and (ii) for the specific case of synchronous periodic task systems, we show that the schedule repeats from the origin. We then present our main result: any feasible schedules of asynchronous periodic task sets using a fixed-priority scheduler are periodic from a specific point. Moreover, we characterize that point and we provide a feasibility interval for those systems.