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The current rate of invasive species introductions is unprecedented, and the dramatic impacts of exotic invasive plants on community and ecosystem properties have been well documented. Despite the pressing management implications, the mechanisms that control exotic plant invasion remain poorly understood. Several factors, such as disturbance, propagule pressure, species diversity, and herbivory, are widely believed to play a critical role in exotic plant invasions. However, few studies have examined the relative importance of these factors, and little is known about how propagule pressure interacts with various mechanisms of ecological resistance to determine invasion success. We quantified the relative importance of canopy disturbance, propagule pressure, species diversity, and herbivory in determining exotic plant invasion in 10 eastern hemlock forests in Pennsylvania and New Jersey (USA). Use of a maximum‐likelihood estimation framework and information theoretics allowed us to quantify the strength of evidence for alternative models of the influence of these factors on changes in exotic plant abundance. In addition, we developed models to determine the importance of interactions between ecosystem properties and propagule pressure. These analyses were conducted for three abundant, aggressive exotic species that represent a range of life histories: Alliaria petiolata , Berberis thunbergii , and Microstegium vimineum . Of the four hypothesized determinants of exotic plant invasion considered in this study, canopy disturbance and propagule pressure appear to be the most important predictors of A. petiolata , B. thunbergii , and M. vimineum invasion. Herbivory was also found to be important in contributing to the invasion of some species. In addition, we found compelling evidence of an important interaction between propagule pressure and canopy disturbance. This is the first study to demonstrate the dominant role of the interaction between canopy disturbance and propagule pressure in determining forest invasibility relative to other potential controlling factors. The importance of the disturbance–propagule supply interaction, and its nonlinear functional form, has profound implications for the management of exotic plant species populations. Improving our ability to predict exotic plant invasions will require enhanced understanding of the interaction between propagule pressure and ecological resistance mechanisms.