Ants figure prominently among the worst invasive species because of their enormous ecological and economic impacts. However, it remains to be investigated which species would be behaviourally dominant when confronted with another invasive ant species, should two species be introduced in the same area. In the future, many regions might have suitable environmental conditions for several invasive ant species, as predicted under climate change scenarios. Here, we explored interactions among several highly invasive ant species, which have been shown to have overlapping suitable areas. The aim of this study was to evaluate the performance in interference competition of seven of the world's worst invasive ant species (Anoplolepis gracilipes, Paratrechina longicornis, Myrmica rubra, Linepithema humile, Lasius neglectus, Wasmannia auropunctata and Pheidole megacephala). We conducted pairwise confrontations, testing the behaviour of each species against each of the six other species (in total 21 dyadic confrontations). We used single worker confrontations and group interactions of 10 versus 10 individuals to establish a dominance hierarchy among these invasive ant species. We discovered two different behavioural strategies among these invasive ants: three species displayed evasive or indifferent behaviour when individuals or groups were confronted (A. gracilipes, Pa. longicornis, M. rubra), while the four remaining species were highly aggressive during encounters and formed a linear dominance hierarchy. These findings contrast with the widespread view that invasive ants form a homogeneous group of species displaying the `invasive syndrome', which includes generally aggressive behaviour. The dominance hierarchy among the four aggressive species may be used to predict the outcome of future competitive interactions under some circumstances. Yet, the existence of several behavioural strategies renders such a prediction less straightforward.