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Motivated by two typical ways to construct multiprocessor systems, matching composition networks and cycle composition networks, we generalize the definition of the Cartesian product of networks and consider the classical diagnosability of the generalized Cartesian product of networks (GCPNs). In this paper, we determine the accurate value of the classical diagnosability of the generalized Cartesian product of networks (GCPNs) under the PMC model and the MM<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mo>*</mo></msup></semantics></math></inline-formula> model.