Acoustic echo cancellers commonly implement linear filters that have to identify as close as possible the impulse response of the acoustic echo path system. However such a system is highly nonlinear, and thus it is reasonable to suppose that a better system identification could be achieved by a nonlinear filter. Volterra filters are well suited for modelling that system but they need in general too many computational resources for a real time implementation. Here we present a novel nonlinear structure which exploits the echo path characteristics and thus is more efficient than conventional Volterra filters. For this structure we have considered two kinds of adaptive algorithms: standard LMS and Affine Projection (AP) algorithms that we adapted to this structure.