A test of linkage that is exact even in small samples is developed for multiple case families, together with large-sample theory for estimation and supplementary tests. Hemochromatosis, insulin-dependent diabetes, and celiac disease are compatible with an intermediate model biased toward recessivity on the penetrance scale, whereas multiple sclerosis favors dominance and unlinked modifiers. Alternatives to the model are complex, and comparison of affected sib pairs with larger sets of relatives provides no critical evidence of epistasis. Problems of sampling and inference are discussed.