With recent rapid advances in mapping of the human genome, including highly polymorphic and closely linked markers, studies of marker associations with disease are increasingly relevant for mapping disease genes. The use of nuclear-family data in association studies was initially developed to avoid possible ethnic mismatching between patients and randomly ascertained controls. The parental marker alleles not transmitted to an affected child or never transmitted to an affected sib pair form the so-called AFBAC (affected family-based controls) population. In this paper, the theoretical foundation of the AFBAC method is proved for any single-locus model of disease and for any nuclear family-based ascertainment scheme. In a random-mating population, when there is a marker association with disease, the AFBAC population provides an unbiased estimate of the overall population (control) marker alleles when the recombination fraction (theta) between the marker and disease genes is sufficiently small that it can be taken as zero (theta = 0). With population stratification, only marker associations present in the subpopulations will be detected with family-based analyses. Of more importance, however, is the fact that, when theta not equal to 0, differences between transmitted parental (patient) marker allele frequencies and non- or never-transmitted parental marker allele frequencies (implying a marker association with disease) can only be observed for marker genes linked to a disease gene (theta < 1/2). Thus, associations of unlinked marker loci with disease at the population level, caused by population stratification, migration, or admixture, are eliminated. This validates the use of family-based association tests as an appropriate strategy for mapping disease genes.