Is it possible to slow the rate of aging, or do biological constraints limit its plasticity? We test this “invariant rate of aging” hypothesis with an unprecedented collection of 39 human and nonhuman primate datasets across seven genera. We first recapitulate, in nonhuman primates, the highly regular relationship between life expectancy and lifespan equality seen in humans. We next demonstrate that variation in the rate of aging within genera is orders of magnitude smaller than variation in pre-adult and age-independent mortality. Finally, we demonstrate that changes in the rate of aging, but not other mortality parameters, produce striking, species-atypical changes in mortality patterns. Our results support the invariant rate of aging hypothesis, implying biological constraints on how much the human rate of aging can be slowed.