An important challenge of invasion biology is to understand how interactions between species traits and ecosystem properties enable alien species to become invasive at particular locations. We investigated how gap dynamics in a tropical rain forest on the island of Réunion affected the invasiveness of alien plants. In the 12 000-m2 study area, alien plants occupied 24.9% of the area of gaps, which represented 5.62% of the forest area, but only 0.8% of the understorey area. The most abundant invasive species was Rubus alceifolius, which formed dense, monospecific stands in the largest gaps (\textgreater 25 m2). Although plants could persist in the shade, a germination experiment revealed that canopy openings were essential for seedling establishment. A cyclone that struck the study area in 2002 caused a temporary thinning of the canopy, increasing light levels to above the threshold needed for germination of R. alceifolius and also stimulating the growth of established plants. We conclude that the ability of this and other alien species to colonize intact lowland tropical rain forest is strongly influenced by the prevailing gap dynamics. Because gaps are also essential for the regeneration of many native trees in our study area, there is a real danger of the forest being progressively degraded by alien plants. There are no simple solutions to controlling species such as Rubus alceifolius, but efforts should be focused mainly upon the larger gaps where the species are most invasive.