Haseman & Elston (1972) introduced a sib pair method using classical regression analysis to detect linkage between a polymorphic marker locus and any quantitative trait locus. Most of the diseases mapped to date follow simple Mendelian, single locus transmission. But there are many familial diseases that do not follow simple Mendelian segregation, for example diabetes, several forms of cancer, etc. In this paper, we extend Haseman and Elston's sib pair method to two unlinked quantitative trait loci each linked to one of two unlinked polymorphic marker loci. For the two-locus epistatic model, we give a general formulation of the complete regression model and details of the regression coefficients in terms of variance components.