Nonnative species richness typically declines along environmental gradients such as elevation. It is usually assumed that this is because few invaders possess the necessary adaptations to succeed under extreme environmental conditions. Here, we show that nonnative plants reaching high elevations around the world are not highly specialized stress tolerators but species with broad climatic tolerances capable of growing across a wide elevational range. These results contrast with patterns for native species, and they can be explained by the unidirectional expansion of nonnative species from anthropogenic sources at low elevations and the progressive dropping out of species with narrow elevational amplitudes--a process that we call directional ecological filtering. Independent data confirm that climatic generalists have succeeded in colonizing the more extreme environments at higher elevations. These results suggest that invasion resistance is not conferred by extreme conditions at a particular site but determined by pathways of introduction of nonnative species. In the future, increased direct introduction of nonnative species with specialized ecophysiological adaptations to mountain environments could increase the risk of invasion. As well as providing a general explanation for gradients of nonnative species richness and the importance of traits such as phenotypic plasticity for many invasive species, the concept of directional ecological filtering is useful for understanding the initial assembly of some native floras at high elevations and latitudes.