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This paper investigates the problem of computing the time-varying {2,3}- and {2,4}-inverses through the zeroing neural network (ZNN) method, which is presently regarded as a state-of-the-art method for computing the time-varying matrix Moore–Penrose inverse. As a result, two new ZNN models, dubbed ZNN23I and ZNN24I, for the computation of the time-varying {2,3}- and {2,4}-inverses, respectively, are introduced, and the effectiveness of these models is evaluated. Numerical experiments investigate and confirm the efficiency of the proposed ZNN models for computing the time-varying {2,3}- and {2,4}-inverses.