Determining whether an alien species is at environmental equilibrium is fundamental to understanding the risk of its continued range expansion, but this is rarely quantitatively assessed. We used experimental transplants within and beyond the current elevation range (~ 0–300 m a.s.l.) of two naturalized succulent plant species, Aeonium arboreum and Aeonium haworthii, to investigate whether they have reached their climatic limits in New Zealand. The two species have similar invasion histories but differ in climatic tolerances in their native ranges, therefore we expected them to differ in their potential to spread within New Zealand. We transplanted individuals of both species along an elevation and precipitation gradient and measured plant growth, mortality and seedling establishment over 2 years. Both species responded strongly and in similar ways to climatic variation along the gradient. Annual frost days was a strong predictor of performance for both species; plants grown at sites with more frost days had lower growth, survival and reproduction. We used our results to predict plant growth, survival and reproduction beyond their current naturalised range. We found that neither species is likely to survive at elevations greater than 300 m a.s.l. and that, while A. haworthii appears to be at or near climatic equilibrium, A. arboreum has the potential for spread further up in elevation. We provide the first evidence of the climatic tolerances of Aeonium sp. in their introduced range, and the risk of their continued spread in New Zealand.