It has been shown that the narrow-band (NB) interference suppression capability of a direct-sequence (DS) spread spectrum system can be enhanced considerably by processing the received signal via a prediction error filter. The conventional approach to this problem makes use of a linear filter. However the binary DS signal that acts as noise in the prediction process is highly non-Gaussian. Thus linear filtering is not optimal. Vijayan and Poor [11J first proposed using a nonlinear approximate conditional mean (ACM) filter of the Masreliez type and obtained significant results. This paper proposes a number of new nonlinear algorithms. Our work consists of three parts. 1) We develop a decision-directed Kaiman (DDK) filter that has the same performance as the ACM filter but a simpler structure. 2) Using the nonlinear function in the ACM and the DDK filters we develop other nonlinear least mean square (LMS) filters with improved performance. 3) We further use the nonlinear functions to develop nonlinear recursive least squares (RLS) filters that can be used independently as predictors or as interference identifiers so that the ACM or the DDK filter can be applied. Simulations show that our nonlinear algorithms outperform conventional ones.