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The invasion of exotic grasses into savannas is occurring globally. Despite threats to ecosystem processes and biodiversity, few studies have investigated factors that facilitate invasion success. * The abundance of the exotic perennial Cenchrus ciliaris buffel grass was assessed across woodland clearings at 46 sites in Queensland, Australia. The influence of fire and grazing on the invasion success were also examined experimentally within 18 sampling stations (including cattle grazed and ungrazed treatment pairs) with unburnt, low-intensity and high-intensity fire treatments. * Mixed-effects logistic regressions suggest that the probability of buffel grass occurring in remnants was predominantly a function of the abundance of buffel grass in adjoining paddocks. The abundance of buffel grass in remnants was greater where the boundaries with clearings faced the prevailing wind adjacent to paddocks with high buffel grass abundance. * There was a significant positive association between buffel grass and tree canopies at approximately half of the sites, and the strength of this association was positively related to the amount of coarse sand in the surface soil. This association was interpreted as nutrient enrichment from litter fall on sandy infertile soils being a requirement for invasion. The invasion of buffel grass at the experimental site accelerated with above-average rainfall after a prolonged drought, and invasion continued even after imposing all combinations of fire and grazing. * Cattle grazing modestly enhanced invasion, relative to the absence of grazing, but this difference was only significant without burning. The occurrence of fire in both the survey and experiment was not associated with enhanced buffel grass invasion. * Invasion of buffel grass may be inevitable over large areas of savanna, especially when abundant rainfall follows periods of drought. However, invasion will be minimized in areas where buffel grass has not been planted, areas without cattle grazing and in areas with low soil fertility. * Synthesis and applications. The invasion of buffel grass accelerates during abundant rainfall after drought and is enhanced by propagule pressure, dispersal trajectories and under trees, probably as a result of nutrient enrichment. Disturbance had little influence on invasion, and there is no support for fire-promoted invasion as predicted by the grass-fire cycle theory.