The nonlinear filter derived by H. V. Poor and R. Vijayan (1988, 1990) is generalized to the case of channels corrupted by impulsive noise. The class of impulsive channels considered includes the Gaussian channel as a special case. The authors exploit the binary nature of the direct-sequence signals to obtain performance using nonlinear filters. A nonlinear modification of the traversal filter, with the coefficients being updated using the least mean square algorithm, is seen to perform significantly better than the standard adaptive linear filter. Further nonlinear modifications of the prediction filters are found for a variety of impulsive channel distribution shapes. It was found that the filters designed for the Gaussian channel perform as well as those tailored to the specific impulsive channels. As a result, the impulsive channels can be approximated by a Gaussian one with no loss in performance.