The technique of direct-sequence (DS) code division multiple access (CDMA) cellular systems has been the focus of increased attention. In this thesis, the problem of narrow-band interference (NBI) cancellation for the DS-CDMA communication systems is considered. It has been shown that the performance of single NBI cancellation for CDMA systems by using the non-linear filtering approach, the so-called DDK filter or the MDK filter, is superior to the one using the linear filtering approach. The main concern of this thesis is to deal with the multiple NBI cancellation. This may occur in some practical application, for instance, in the 2.4GHz CDMA system, the bluetooth and wireless LAN may exist in the same frequency band with different power ratio. In this thesis, the nonlinear filtering with fast convergence least square (LS) algorithms, viz., the modified inverse QRD-RLS (IQRD-RLS) and the interior point (IP) LS algorithms, are devised for multiple NBI cancellation in the multi-user CDMA system. In fact, the IQRD-RLS and the IP LS algorithms are known to have better numerical stability and convergence property in the RLS family. Since in the non-linear MDK filter with the IQRD-RLS algorithm, the prediction error £`k,k-1 used in the conventional IQRD-RLS is replaced by the nonlinear function of £l(£`k,k-1), and is defined to as the modified IQRD-RLS algorithm. The merits of the proposed algorithms are verified via computer simulation. We showed that the performance of our proposed algorithms outperformed the one using the conventional nonlinear filtering approach with LMS algorithm, in terms of convergence property and the signal-to-noise ratio improvement (SNRI).