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Aggregate scheduling is one of the most promising solutions to the issue of scalability in networks, like DiffServ networks and high speed switches, where hard QoS guarantees are required. For networks of FIFO aggregate schedulers, the main existing sufficient conditions for stability (the possibility to derive bounds to delay and backlog at each node) are of little practical utility, as they are either relative to specific topologies, or based on strong ATM- like assumptions on the network (the so- called ”RIN” result), or they imply an extremely low node utilization. We use a deterministic approach to this problem. We identify a non linear operator on a vector space of finite (but large) dimension, and we derive a first sufficient condition for stability, based on the super-additive closure of this operator. Second, we use different upper bounds of this operator to obtain practical results. We find new sufficient conditions for stability, valid in an heterogeneous environment and without any of the restrictions of existing results. We present a polynomial time algorithm to test our sufficient conditions for stability. We show that with leaky-bucket constrained flows, the inner bound to the stability region derived with our algorithm is always larger than the one determined by all existing results. We prove that all the main existing results can be derived as special cases of our results. We also present a method to compute delay bounds in practical cases.