The general linear structural equation model is applied to problems in human genetics where there may be more than one measured phenotype per individual. A modeling convention, termed conditional associations, is developed to extend the general linear model so that it can handle the unique problems in human genetic models that arise from the pairing up of individuals or families under assortment between mates and the assortative placement of adoptees. Formulas are presented to generate expected covariance matrices for assortment or assortative placement on many variables simultaneously. It is demonstrated that all linear models in human genetics can be reduced in form to two fundamental equations. An algorithm is presented that will allow the application of these two equations to linear modeling in human genetics.