Sex-specific senescence has been commonly reported in highly dimorphic and polygynous species. However, whether between-sex differences in senescence occur in monogamous and monomorphic species is poorly known. In this study, we used an extensive dataset of 20 years of mass measurements on free-ranging male and female Alpine marmots (Marmota marmota), a medium-sized, long-lived, social and hibernating mammal, to assess sex-specific patterns of senescence in body mass. We tested for the occurrence of both a decrease in body mass scaled to absolute age (called chronological senescence) and a decrease in body mass scaled to individual age at death (called terminal decline). Whereas males showed evidence of both chronological senescence and terminal decline in body mass, females did not show any detectable senescence in body mass. This unexpected between-sex difference of senescence in a species subject to weak sexual selection might be shaped either by costs of an asymmetric intra-sex competition for mates or by costs of social thermoregulation.