This study deals with the design and analysis of an adaptive array processor in which the individual filters consist of tapped delay lines and adjustable gains. The gains are adjusted automatically by an iterative procedure which is a modified form of the stochastic approximation method of Robbins and Monro. The criterion for optimality is that the mean-square error between filter output and an ideal signal be a minimum. However, it is shown that the ideal signal need not be available to the processor; it suffices that the signal autocorrelation function and spatial direction be available. General expressions are obtained for convergence of the iterative algorithm, and an explicit expression for an upper bound on the rate of convergence is derived. System performance is analyzed by considering a noise field consisting of a spatially isotropic component and a single directional component. It is shown that the adaptive system eventually acts to eliminate the effect of the directional component. The theoretical behavior of the system has been verified experimentally using actual sonar data and a six-element array. © 1971, Acoustical Society of America. All rights reserved.