Pearson [Philos Trans R Soc Lond [A] 200:1-66, 1903], Mendell and Elston [Biometrics 30:41-57, 1974], and Rice et al. [Biometrics 35:451-459, 1979] approximated the likelihood of the multifactorial model on a dichotomous phenotype by a procedure of successive univariate computation and conditioning. Hasstedt [Pap: Pedigree Analysis Package, Rev. 3. 1989] and Demenais [Am J Hum Genet 49:773-785, 1991] extended the algorithm to include a major locus. Here I extend the algorithm to polychotomous, quantitative, and multivariate phenotypes, add a major locus to the model, and describe and evaluate the accuracy of an approximation of the resulting variance components/major locus model.