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1. Successful poleward shifts of plant species ranges as a result of climate change will depend on interactions between migrating species and the communities they invade. Although poleward migration may be constrained by slow long-distance dispersal into suitable habitat, the invasion resistance of a plant community is expected to depend on the timeframe available for species- and genetic-level compositional shifts. 2. We tested whether range shifts of Bromus erectus and Brachypodium pinnatum, two dominant grasses of calcareous grasslands in the southern UK with different phenologies and competitive abilities, are limited by dispersal and whether local plant communities are able to adapt to changes in climate conditions and resist invasion from novel species. We added seeds of the two species to an infertile grassland in northern England, where both species are currently absent and where winter warming and summer drought have been simulated for short (1 year) and long (15 years) durations. 3. We predicted that seed addition would lead to higher establishment of the two species in grassland plots subjected to artificial winter warming than in plots with imposed summer drought, and we expected that invasion resistance of the extant grassland community would be higher in long-term than in short-term climate manipulations. 4. Warming induced earlier seedling emergence in both species and resulted in higher invader above-ground biomass at the end of the first growing season. Summer drought did not affect the invasion success of Bromus but it offset the beneficial effects of winter warming in Brachypodium. Invader performance was similar in communities with long- and short-term climate manipulations. 5. Synthesis. ‚Climate induced poleward shifts will proceed even if slow long-distance dispersal of migrating species allows extant communities to adapt to a new climate regime. Asynchrony between the phenology of migrating species and seasonal resource use by invaded communities are likely to amplify migration success.