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Automatic speaker identification ASI is to determine the identity of an individual among a group of known people. From the recorded voice samples, it must determine which speaker spoke of the base. In this paper we are interested at the classification phase of the ASI system and we presented how to implement the multilayer perceptrons (MLP) and radial basis functions (RBF) Neural Network in the classification step of the ASI system, and a performance comparison study between the MLP and RBF to support the classification activity, by estimating the probability density functions required by Bayesian classifiers within a system of ASI. Advantages and disadvantages of each method are discussed and the effects introduced by the speaker's number for the ASI system complexity were taken into account. During the various experiments, the Japanese vowels database and the Numenta Speakers database are used to validate our comparative study of RBF and MLP.