Abstract: A non-linear adaptive filter is described having a linear filter connected in parallel with a non-linear filter. The linear filter provides fast adaption until it has modelled the linear contribution of each coefficient. Thereafter the non-linear filter continues to adapt until the error signal has been reduced to an acceptable level.In a preferred embodiment a plurality of unit delay devices provide taps to sub-processing units each of which is arranged to be adapted according to a linear algorithm during an initial part of a training period, and to a non-linear algorithm after said initial part.The filter has particular use in echo cancellers for data modems.