This paper describes the extension of the maximum likelihood spectrum estimation procedure  to the multichannel case and compares its properties experimentally with other high resolution methods for multichannel 2-D spectrum analysis [2,3]. The procedure begins with a multichannel optimum filtering problem and extends the original procedure to the estimation of the entire spectral matrix. In so doing it formally encompasses both the original single channel problem and various separate attempts to develop maximum likelihood cross spectral estimates for two random processes [4,5]. The paper also considers the so-called improved maximum likelihood method of Lim and Dowla  and develops it for the multichannel case. The methods are applicable to both one-dimensional and multidimensional multichannel spectral estimation.