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The nonlinear distortion of an acoustic signal caused by the nonlinearity of a power amplifier and/or loudspeaker may give rise to a nonlinear component in acoustic echo cancellation systems. A conventional acoustic echo canceller (AEC) using linear adaptive filtering is not able to eliminate the nonlinear echo component to a satisfactory degree. In this paper, we present a nonlinear echo cancellation technique that uses a nonlinear transformation along with a regular linear adaptive filter for the compensation of the nonlinear echo component. A raised-cosine function is used to derive the nonlinear transformation and the parameters of the nonlinear compensator are updated to adapt to the nonlinearity of the unknown distorting path. The proposed method is simulated in conjunction with the conventional normalized least mean squared algorithm, showing a superior performance of the proposed acoustic echo canceller.