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Abstract: In this work, local stability on the initialization phase of nonlinear autoregressive with exogenous inputs multilayer perceptrons (NARX MLP) and radial basis functions (NARX RBF) neural networks is studied. It will be shown that the selection of adequate ranges for the initial weights is related with local stability of the network in its initial stage. As a result, quantitative limits for the initial weights are established that guarantee local stability and accelerate the learning process. These theoretical developments have been tested in experiments which corroborate the improvements achieved with the proposed initialization methods. [Copyright &y& Elsevier]