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Strong diagnosability is a more precise concept for measuring the reliability of multiprocessor systems than the traditional global measurement. In this paper, we study the strong diagnosability of multiprocessor systems under the PMC model. Our main objective is to determinate the strong diagnosability of two wide classes of networks, namely regular networks and product networks, subject to certain conditions. Based on our results, we demonstrate the strong diagnosability of several well-known networks, including variants of hypercubes and many others.