Adaptive equalizers are used in most modern communication systems to compensate for channel distortion in order to achieve reliable data transmission. Quite a steady research in this ¯eld has been made in the literature for over the last four decades and still remain a subject of ongoing investigation. This thesis present adaptive equalization scheme using a new power-of-two quantizer algorithm. The new al- gorithm, which is non-mean-square based, provides a simpli¯cation to least mean fourth (LMF) algorithm and also addresses the non-optimal performance problem of power-of-two quantizer based least mean square (LMS) algorithm when used in non- Gaussian environment. From the moment based analysis of the LMF algorithm, we outline the basic idea behind the development of this new algorithm as well as the necessary assumptions and identi¯able conditions required for its convergence behaviour. Derivations of pertinent parameters and the convergence analysis of the new algorithm are presented and the result of simulation carried out veri¯es the the- oretical predictions.