The power to detect linkage by the LOD-score method is investigated here for diseases that depend on the effects of two genes. The classical strategy is, first, to detect a major-gene (MG) effect by segregation analysis and, second, to seek for linkage with genetic markers by the LOD-score method using the MG parameters. We already showed that segregation analysis can lead to evidence for a MG effect for many two-locus models, with the estimates of the MG parameters being very different from those of the two genes involved in the disease. We show here that use of these MG parameter estimates in the LOD-score analysis may lead to a failure to detect linkage for some two-locus models. For these models, use of the sib-pair method gives a non-negligible increase of power to detect linkage. The linkage-homogeneity test among subsamples differing for the familial disease distribution provides evidence of parameter misspecification, when the MG parameters are used. Moreover, for most of the models, use of the MG parameters in LOD-score analysis leads to a large bias in estimation of the recombination fraction and sometimes also to a rejection of linkage for the true recombination fraction. A final important point is that a strong evidence of an MG effect, obtained by segregation analysis, does not necessarily imply that linkage will be detected for at least one of the two genes, even with the true parameters and with a close informative marker.