The analysis of covariance structures (Jöreskog, 1973) is adapted to the simultaneous maximum likelihood estimation of genetical and environmental factor loadings and specific variances. The goodness of fit is tested by chi square and standard errors of parameter estimates can be obtained. Any linear model used in univariate genetical analyses can be extended to the multivariate case. Most biological hypotheses about the relationships between variables can be specified by a variety of factor models. Individual parameters can be given fixed values or set to zero and hypotheses concerning the congruence of genetical and environmental correlations can be tested. The method is illustrated with published twin data on cognitive abilities.