Behavioural sex-role reversal occurs when males and females exchange their standard roles in territorial defence or parental care. One circumstance under which sex-role reversal may occur is when males are a limiting resource, so that females have to compete for access to mates. Here we report on male rarity and male and female behaviour of species within the damselfly genus Nesobasis, endemic to Fiji. Earlier reports suggested that, in some members of this genus, males were seldom observed and that females of these species were consequentially territorial, a phenomenon described as ‘sex-role reversal’. Quantitative estimation of the ratio of adult males to females at 15 localities in 13 Nesobasis species (1489 individuals) indicated that males were extremely rare in some species, yet common in others. This interspecific variability in male rarity cannot be explained by elevation or habitat. Formal observations of three species with abundant males revealed that males of these species were highly territorial: they physically challenged intruders while remaining within a confined area. By contrast, in three species where males were consistently rare or absent, females were not territorial: instead, they moved widely and were primarily engaged in oviposition. While we do not know the underlying reason for the unusual rarity of males at oviposition sites in some species, it is clear that this rarity has not provided sufficient selection pressure to generate genuine sex-role reversal.