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We discuss a novel design methodology of self-organizing approximator technique (self-organizing polynomial neural networks) (SOPNN) in the framework of genetic algorithm (GA). SOPNN dwells on the ideas of group method of data handling (GMDH). Its each node exhibits a high level of flexibility and realizes a polynomial type of mapping between input and output variables. But the performances of SOPNN depend strongly on a few factors. They are number of input variables available to the model, number of input variable and type (order) of the polynomials to each node. In most cases, these factors are determined by the trial and error method. Moreover, SOPNN algorithm is a heuristic method so it does not guarantee that the obtained SOPNN is the best one for nonlinear system modeling. Therefore, more attention must be paid to solve the drawbacks. We alleviate these problems by using GA. Comparisons with other modeling methods and conventional SOPNN show that the proposed design method has better performance.