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This paper reviews basic concepts of GMDH as developed by Ivakhnenko and his coworkers in the U.S.S.R. The attractive features of GMDH are: (i) It determines the structure of nonlinear systems. (ii) It separates fitting and checking sets to avoid the pitfalls of overfitting. (iii) It can employ multicriteria objective function for model validation. These and other features of GMDH, such as networks of polynomials and layering concepts are examined critically and compared with other techniques used in Nonlinear System *****Identification. Examples are presented to illustrate the application of GMDH to industrial and environmental modeling problems.