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Standard approaches for the cancellation of acoustic echoes in telecommunication systems assume that the echo path to be identified can be modeled by a linear system. However, in applications such as echo cancellation for mobile communication terminals, non-negligible nonlinear distortions are introduced by loudspeakers and their amplifiers, resulting in a significant degradation of the performance of purely linear approaches. In this contribution we consider so-called power filters in order to cope with these kinds of nonlinear echo paths. By combining time-domain orthogonalization methods with a DFT-domain implementation of power filters we derive corresponding quasi-complete orthogonalized versions. As the statistical properties of speech input are non-stationary, the orthogonalization must follow this time-variance, too. Furthermore, we introduce a step-size control for the adaptation of the equivalent orthogonalized structure. Experiments with real hardware show that, with the proposed nonlinear approach, an increase in echo attenuation can be achieved, if the loudspeaker system introduces saturation-type nonlinearities in the echo path.