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We describe a broad class of family‐based association tests that are adjusted for admixture; use either dichotomous or measured phenotypes; accommodate phenotype‐unknown subjects; use nuclear families, sibships or a combination of the two, permit multiple nuclear families from a single pedigree; incorporate di‐ or multi‐allelic marker data; allow additive, dominant or recessive models; and permit adjustment for covariates and gene‐by‐environment interactions. The test statistic is the covariance between a user‐specified function of the genotype and a user‐specified function of the trait. The distribution of the statistic is computed using the appropriate conditional distribution of offspring genotypes that adjusts for admixture. Genet. Epidemiol. 19(Suppl 1):S36–S42, 2000. © 2000 Wiley‐Liss, Inc.