* Information about the incidence and magnitude of local adaptation can help to predict the response of natural populations to a changing environment, and should be of particular interest in arctic and alpine environments where the effects of climate change are expected to be severe. * To quantify adaptive differentiation in the arctic-alpine perennial herb Arabis alpina, we conducted reciprocal transplant experiments for 3 yr between Spanish and Scandinavian populations. At the sites of one Spanish and one Scandinavian population, we planted seedlings representing two Spanish and four Scandinavian populations, and recorded survival, flowering propensity and fecundity. The experiment was replicated in two subsequent years. * The results demonstrate strong adaptive differentiation between A. alpina populations from the two regions. At the field site in Spain, survival and fruit production of Spanish populations were higher than those of Scandinavian populations, while the opposite was true at the site in Scandinavia, and these differences were consistent across years. By comparison, fitness varied little among populations from the same region. * The results suggest that the magnitude and geographical scale of local adaptation need to be considered in predictions of the effects of global change on the dynamics of arctic and alpine plant populations.