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This paper investigates the statistical behavior of two gradient search adaptive algorithms for identifying an unknown nonlinear system comprised of a discrete-time linear system H followed by a zero-memory nonlinearity g(/spl middot/). The input and output of the unknown system are corrupted by additive independent noises. Gaussian models are used for all inputs. Two competing adaptation schemes are analyzed. The first is a sequential adaptation scheme where the LMS algorithm is first used to estimate the linear portion of the unknown system. The LMS algorithm is able to identify the linear portion of the unknown system to within a scale factor. The weights are then frozen at the end of the first adaptation phase. Recursions are derived for the mean and fluctuation behavior of the LMS algorithm, which are in excellent agreement with Monte Carlo simulations. When the nonlinearity is modeled by a scaled error …