Volterra-series models of magnetic-saturation recording channels are used to derive readback structures that compensate for channel nonlinearities. These structures are based on a canceler of linear and nonlinear channel distortions, and can achieve significant improvement in terms of mean-square error and error probability. Proper operation of the canceler requires reliable preliminary decisions to be taken on the information symbols. These decisions are obtained by passing the received signal through a linear equalizer, then processing the equalized signal through a symbol-by-symbol detector or a Viterbi detector. By using the data obtained in [4] for magneto-resistive heads, it was found that symbol-by-symbol preliminary detection performs adequately. A Volterra model was also obtained experimentally for the recording channel generated by magneto-inductive heads that exhibit higher-order nonlinear effects. In order to recover data from this highly distorted channel the preliminary detection scheme needs a 4-state Viterbi detector.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>