Human females stop reproducing long before they die. Among other mammals, only pilot and killer whales exhibit a comparable period of post-reproductive life. The grandmother hypothesis suggests that kin selection can favour post-reproductive survival when older females help their relatives to reproduce. But although there is an evidence that grandmothers can provide such assistance, it is puzzling why menopause should have evolved only among the great apes and toothed whales. We have previously suggested (Cant & Johnstone 2008 Proc. Natl Acad. Sci. USA 105, 5332-5336 (doi:10.1073/pnas.0711911105)) that relatedness asymmetries owing to female-biased dispersal in ancestral humans would have favoured younger females in reproductive competition with older females, predisposing our species to the evolution of menopause. But this argument appears inapplicable to menopausal cetaceans, which exhibit philopatry of both sexes combined with extra-group mating. Here, we derive general formulae for 'kinship dynamics', the age-related changes in local relatedness that occur in long-lived social organisms as a consequence of dispersal and mortality. We show that the very different social structures of great apes and menopausal whales both give rise to an increase in local relatedness with female age, favouring late-life helping. Our analysis can therefore help to explain why, of all long-lived, social mammals, it is specifically among the great apes and toothed whales that menopause and post-reproductive helping have evolved.