Multiple invasive species have now established at most locations around the world, and the rate of new species invasions and records of new invasive species continue to grow. Multiple invasive species interact in complex and unpredictable ways, altering their invasion success and impacts on biodiversity. Incumbent invasive species can be replaced by functionally similar invading species through competitive processes; however the generalized circumstances leading to such competitive displacement have not been well investigated. The likelihood of competitive displacement is a function of the incumbent advantage of the resident invasive species and the propagule pressure of the colonizing invasive species. We modeled interactions between populations of two functionally similar invasive species and indicated the circumstances under which dominance can be through propagule pressure and incumbent advantage. Under certain circumstances, a normally subordinate species can be incumbent and reject a colonizing dominant species, or successfully colonize in competition with a dominant species during simultaneous invasion. Our theoretical results are supported by empirical studies of the invasion of islands by three invasive Rattus species. Competitive displacement is prominent in invasive rats and explains the replacement of R. exulans on islands subsequently invaded by European populations of R. rattus and R. norvegicus. These competition outcomes between invasive species can be found in a broad range of taxa and biomes, and are likely to become more common. Conservation management must consider that removing an incumbent invasive species may facilitate invasion by another invasive species. Under very restricted circumstances of dominant competitive ability but lesser impact, competitive displacement may provide a novel method of biological control.