Local adaptation at range edges influences species' distributions and how they respond to environmental change. However, the factors that affect adaptation, including gene flow and local selection pressures, are likely to vary across different types of range edge. We performed a reciprocal transplant experiment to investigate local adaptation in populations of Plantago lanceolata and P. major from central locations in their European range and from their latitudinal and elevation range edges (in northern Scandinavia and Swiss Alps, respectively). We also characterized patterns of genetic diversity and differentiation in populations using molecular markers. Range-centre plants of P. major were adapted to conditions at the range centre, but performed similarly to range-edge plants when grown at the range edges. There was no evidence for local adaptation when comparing central and edge populations of P. lanceolata. However, plants of both species from high elevation were locally adapted when compared with plants from high latitude, although the reverse was not true. This asymmetry was associated with greater genetic diversity and less genetic differentiation over the elevation gradient than over the latitudinal gradient. Our results suggest that adaptation in some range-edge populations could increase their performance following climate change. However, responses are likely to differ along elevation and latitudinal gradients, with adaptation more likely at high-elevation. Furthermore, based upon these results, we suggest that gene flow is unlikely to constrain adaptation in range-edge populations of these species.