Haseman and Elston (HE)[1972] proposed a method to detect quantitative trait loci by linkage to a marker. The squared sib-pair trait difference is regressed on the proportion of marker alleles the pair is estimated to share identical by descent: a significantly negative regression coefficient suggests linkage. It has been shown that a maximum likelihood method that directly models the sib-pair covariance has more power. This increase in power can also be obtained using the HE regression procedure by changing the dependent variable from the squared difference to the mean-corrected product of the sibs' trait values. Multiple sibs in a sibship can be accommodated by allowing for the correlations between pairs of products in a generalized least squares procedure. Multiple trait loci, including epistatic interactions, involve only multiple linear regression. Multivariate traits can use the method of Amos et al.[1990] to find the linear function of the traits that maximizes the evidence for linkage, which now leads more simply to a test of significance. Multiple markers can be the basis of a multipoint analysis. Results of simulation studies for a continuous trait are presented that investigate Type I error and power. A similar general scheme can be used to study affected sib pairs, testing whether their identity by descent sharing probabilities are greater than would be expected in the absence of linkage, and to study other types of relative pairs. Genet. Epidemiol. 19: 1–17, 2000.© 2000 Wiley-Liss, Inc.