Adult dragonflies (Anisoptera) and damselflies (Zygoptera) are amongst the most accomplished flying insects on the planet. The main functions of spatial displacement by flight in these insects are well understood (e.g., escape from predators, foraging, reproduction, thermoregulation), but whether males and females exhibit different degrees of flight agility across species—and why—is by contrast, poorly understood. This is important because flight agility may differ between males and females due to the costs imposed on females by the high levels of sexual selection and sexual conflict observed in certain species. Here we used a wing parameter to estimate sexual dimorphism in flight agility in 63 Odonata taxa. We then used a phylogenetic comparative method to investigate whether sexual dimorphism in flight agility differed between (i) Anisoptera and Zygoptera, and (ii) mating systems (non-territorial, territorial). Our results first show that the distribution of sexual dimorphism in flight agility between Odonata families is non-random. Second, our results suggest that whereas sexual dimorphism in flight agility is not different between non-territorial and territorial Anisoptera, in Zygoptera it is predominantly female-biased in non-territorial species, and male-biased in territorial ones. There may be important behavioural and mating differences between Anisoptera and Zygoptera which explain the different needs of agility observed between suborders and mating systems.