Any population whose members are subject to extrinsic mortality should exhibit an increase in mortality with age. Nevertheless, the prevailing opinion is that populations of adult damselflies and dragonflies do not exhibit such senescence. Here, we challenge this contention by fitting a range of demographic models to the data on which these earlier conclusions were based. We show that a model with an exponential increase in age‐related mortality (Gompertz) generally provides a more parsimonious fit than alternative models including age‐independent mortality, indicating that many odonates do indeed senesce. Controlling for phylogeny, a comparison of the daily mortality of 35 odonate species indicates that although male and female mortalities are positively correlated, mortality tends to be higher in males of those species that exhibit territoriality. Hence, we show for the first time that territoriality may impose a survivorship cost on males, once the underlying phylogenetic relationships are accounted for.