Traditional adaptation algorithms for acoustic echo cancellers are sufficiently robust to give satisfying performance even in the presence of nonlinear distortions, e.g. those induced by low-cost audio equipment in speech communication products for the consumer market. However, the performance of echo compensation can be improved if special measures are taken to acount for nonlinear behaviour in the electro-acoustic transmission system. To this end, a compensation method for memoryless nonlinearities, as encountered in overdriven amplifiers, is presented. Measurements demonstrate that the echo return loss enhancement can be improved without slowing down convergence. It is thus posssible to compensate the nonlinear effects of cheap audio components with few additional operations in the digital part of the device.