The children of twins (COT) design has been proposed as an alternative to the adoption study to resolve the direct effects of parental treatment from secondary parent–child association due to genetic factors. The basic analytical approach compares the parent–offspring correlation with the correlation between children and the monozygotic (MZ) twins of their parents. We show that a significant difference between these correlations does not imply direct environmental causality when the measured parental treatment in question is dyadic, that is, influenced by both parents even when mating is random. Nongenetic causal effects yield very similar patterns of correlation to secondary genetic effects on dyadic treatment variables. The fact that many candidate environments, such as parental divorce, are dyadic gives reason to question the interpretation of their correlations with behavior in the children of twins.