Bats live substantially longer than any other similar-sized mammal despite high metabolic rates during flight. The underlying causes for the longevity of bats and the question whether bats exhibit signs of senescence – a progressive deterioration in performance – are still unclear. Here, we describe rates of senescence in individual annual fitness, survival and reproduction using survival and recruitment data collected over an 18-yr period from 77 males and 81 females in a wild population of Saccopteryx bilineata (greater sac-winged bat), a polygynous species inhabiting colonies where female groups are defended each by a territorial male. In individuals older than 4 yr of age, individual fitness contribution, survival and recruitment declined with increasing age in males but not in females. Rates of senescence in annual individual fitness and in reproduction of males were at least an order of magnitude higher than those of females. This finding might be explained by the ‘disposable soma theory’ that attributes senescence to an optimal allocation of resources to somatic maintenance and competing traits such as reproduction. The rate of senescence in the survival of males was also significant but of the same order of magnitude as the (non-significant) rate of females. Unlike many other polygynous mammals, greater sac-winged bats show little overt male–male competition. As senescence in survival was only weak in males, our results are consistent with the theories for polygynous mammals, which view the trade-off between male investment in physical traits for intense male–male competition against survival as a major source of the decline of male survival with age. This is the first study to demonstrate sex-specific senescence rates in a wild population of a small, long-lived mammalian species.