Because families have varying numbers of offspring, the maximum likelihood estimators of the interclass, or parent-offspring, and intraclass, or offspring-offspring, correlations are difficult to compute (Srivastava, 1984). For this reason, alternative estimators have been proposed, which are not necessarily asymptotically efficient. However, maximum likelihood estimators of the inter- and intraclass correlations in families of constant size can be obtained in closed form, so that asymptotically efficient estimators of these correlations are obtained here as weighted sums of the subsample estimators. As an added advantage, one can test various models that express parent-offspring or offspring-offspring correlations as functions of family size.