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In this correspondence, we discuss the stability of scheduling algorithms for input-queueing (IQ) and combined input/output queueing (CIOQ) packet switches. First, we show that a wide class of IQ schedulers operating on multiple traffic classes can achieve 100% throughput. Then, we address the problem of the maximum throughput achievable in a network of interconnected IQ switches and CIOQ switches loaded by multiclass traffic, and we devise some simple scheduling policies that guarantee 100% throughput. Both the Lyapunov function methodology and the fluid modeling approach are used to obtain our results.