Data from 949 families of Caucasian and 400 families of Japanese ancestry who took part in the Hawaii Family Study of Cognition were used to ascertain the associations of parental cognitive ability, parental education and paternal occupation with offspring cognitive ability. In particular, analyses were focused on testing the possible moderating effects of parental socioeconomic status on the familial transmission of cognitive abilities. Parental cognitive ability was substantially associated and parental education and paternal occupation only trivially associated with offspring performance. In contrast to the findings of Turkheimer et al. (2003), there was no evidence in these data that familiality for cognitive abilities was lower in the lower as opposed to upper levels of socioeconomic status. These results were consistent across measures, ethnicity and sex of offspring.