This proposal is concerned with the development and analysis of a class of robust adaptive filtering algorithms which can offer effective performance in an environment of impulsive and other non- gaussian noise. These filters are termed Order Statistic Least Mean Square (OSLMS) adaptive filters. A special case of this class is the Median LMS (MLMS) algorithm, derived from the familiar LMS algorithm by replacing the instantaneous measurements of the gradient of the mean square error performance surface, used by the LMS filter, with the sample median of that quantity.