The transmission disequilibrium test (TDT), originally developed for mapping disease genes, has recently been extended to identify quantitative trait loci (QTL). For quantitative traits important for human health, generally multiple QTLs are involved. In the investigation of the statistical properties of the TDT, background polygenes (QTLs other than the QTL under test) generally have not been explicitly considered. The effects of background polygenes on the statistical properties of the TDT are thus largely unknown. Investigation of these effects will provide more realistic analyses of the statistical properties of the TDT under biologically plausible situations, and thus provide more accurate guidelines on the application of the TDT in practice. A general TDT (TDTG) has been developed to test linkage of a QTL in nuclear families that may be composed of more than one heterozygous parent and multiple children. Using the TDTG as an example, we develop an analytical method to investigate the effects of background polygenes on the power of the TDT. The accuracy of our analytical method is validated by computation simulations. We found that the power of the TDTG is increased with background polygenes when more than one child is employed in nuclear families, and the effect is stronger with more children per family recruited for study. The power of the TDTG increases dramatically when the number of children recruited from each nuclear family increases from one to two or from two to three. The type one error rate is not affected by the presence of background polygenes. The results of this study should be of theoretical significance in generalizing the investigation of the TDT to biologically plausible situations with background polygenes. They should also be of practical values in providing guidance on the recruitment of nuclear families with multiple children with the TDTG. Genet. Epidemiol. 21:243–265, 2001. © 2001 Wiley-Liss, Inc.