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The purpose of this work is to introduce engineers and researchers to the field of nonlinear adaptive system identification. The author describes the general area, and presents the Volterra model approach and the discrete Wiener model approach. The performances of the two model approaches are compared.The book focuses on polynomial types of nonlinearities for which the Volterra and Wiener approaches are well-suited. Further, extensive coverage is given to System Identification applications of the adaptive methods. These methods can be applied to other applications of adaptive nonlinear processes. The book includes recent research results in the area of adaptive nonlinear system identification from the author and other active researchers in the field.