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Audio watermarking systems for protecting ownership rights may need to withstand attacks that include passing the watermarked audio signal through nonlinear systems, with or without memory. In this work we present an approach by which the memoryless nonlinearity is modeled by a piecewise approximation of the nonlinear function using a relatively small number of linear segments. It is shown that the adaptive LMS framework can be used to estimate the segment slopes. Furthermore, it is shown that the LMS-based identification processes of both the linear system coefficients (modeled as an FIR filter) and the memoryless nonlinearity parameters (slopes) can be combined into a simple and efficient single process. In addition to its ability to handle a cascade of linear (L) and nonlinear (N) components (both L-N and N-L cascade arrangements) this approach can be extended in a modular way to handle other cascade arrangements like N-L-N, L-N-L, N-L-N-L, etc.