Differential female longevity is so far unexplained in evolutionary terms. The theory of evolutionarily necessary aging which goes back to Wallace appears to be up to the task. In this theory, aging minimizes competition between forebear and offspring. The aging equation which is implicit contains the well-known empirical Gompertz law as a special case. Moreover, its parameters are automatically sex-specific. It is shown that the slower aging of the female members of two species of mammals, humans and sperm whales, can be 'predicted' on the basis of this equation. A prediction of effective human monogamy under archaic conditions is obtained as a corollary. The analogous if opposite prediction for sperm whales (strong promiscuity) is empirically testable.