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A gradient-type algorithm for the parametric identification of a nonlinear structure (L-N-L), comprising of a linear FIR filter in front of a set of nonlinear functions is investigated with respect to its robustness. The set of nonlinear functions is represented by a weighted sum of basis functions. Specifically, a feedback structure, describing the update-part of the adaptive algorithm, is developed. Using the small gain theorem, the stability of this feed-back structure and thus the robustness of the adaptive algorithm is investigated. Step-size conditions for local and global convergence are presented. As an application example, this structure is utilized to model a nonlinear power amplifier for mobile communications.