Abstarct: Presence of nonlinear component of circuit affects the performance of conventional acoustic echo canceller and has negative impact on the quality of voice telecommunication. To solve this problem, nonlinear acoustic echo cancellers are used which are obtained from modeling of nonlinear paths and sound improvement. In this thesis, a new class of nonlinear adaptive algorithms baxsed on functional lixnk adaptive filters is proposed for nonlinear models of acoustic channel. Due to the flexible architecture, these algorithms are an efficient solutions to model effective nonlinearities on acoustic signal. Chebyshev, trigonometric and Legendre mathematical functions are used for input expansion. The separation between the linear and nonlinear components in collaborative and split adaptive filters, leading to two different adaptive filters. The linear one with the purpose of estimating the acoustic impulse response, and the nonlinear one just with duty of nonlinearities modeling which is robust against various degrees of nonlinearity. With this method, performance of convergence is improved dramatically. The Collaborative model with prevention of gradient nonlinear noises when the system is linear, has a good performance in any echo conditions. Thus, architectures baxsed on this foundation can be considered as an effective solution for acoustic channels model. The results obtained in this thesis show that adaptive algorithms baxsed on Chebyshev and trigonometric functional lixnks have a good performance for nonlinear echo cancellation purpose and can correct the echo up to 50dB.