This paper describes three IBM 360/65 computer programs--GEN1, GEN2 and GEN3--for a generalized factor analysis based on residual covariance matrices of prescribed structures. Programs GEN 2 and GEN 3 are successive elaborations of GEN1, with successively smaller limits on the maximum dimensions of problems to be submitted. Program GEN1 uses the generalized Thomson algorithm for principal factor analysis. Program GEN 2 adds to this a Thomson-type algorithm for a generalized Lawley-Rao maximum likelihood solution. Program GEN3 adds, further, the Fletcher and Powell procedure for obtaining an extremum of a function. Program GEN2 allows the user to prescribe a number of iterations of the principal factor procedure, to provide a starting point for the generalized Thomson-type iterations for a maximum likelihood solution. It also computes a chi-quare value, given the number of cases, to test the hypothesis that the number of major factors is greater than that prescribed in a given run of the problem, and computes major factor scores if desired. Program Gen 3 differs from Gen 2 only by adding the option of calling the Fletcher-Powell subroutine of Joreskog, after prescribed numbers of iterations of the principal factor algorithm and Thomson algorithm (the latter number may be zero.). The theories behind the programs and the expected outcomes, are discussed briefly. Their objectives, and input data decks are presented in detail. The actual programs are included in the appendices.