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This paper presents analytical, numerical, and experimental results for a stochastic gradient adaptive scheme that identifies a polynomial-type nonlinear system with memory for noisy output observations. The analysis includes the computation of the stationary points, the mean square error surface, and the stability regions of the algorithm for Gaussian data. Convergence of the mean is studied using L/sub 2/ and Euclidian norms. Monte Carlo simulations confirm the theoretical predictions that show a small sensitivity to the observation noise. An application is presented for the identification of a nonlinear time-delayed feedback system.