Parapatry is a biogeographical term used to refer to organisms whose ranges do not overlap, but are immediately adjacent to each other; they only co-occur – if at all – in a narrow contact zone. Often there are no environmental barriers in the contact zones, hence competitive interaction is usually advocated as the factor that modulates species distribution ranges. Even though the effects of climate change on species distribution have been widely studied, few studies have explored these effects on the biogeographical relationships between closely related, parapatric, species. We modelled environmental favourability for three parapatric hare species in Europe – Lepus granatensis, L. europaeus and L. timidus – using ecogeographical variables and projected the models into the future according to the IPCC A2 emissions scenario. Favourabilities for present and future scenarios were combined using fuzzy logic with the following aims: (i) to determine the biogeographical relationships between hare species in parapatry, that is L. granatensis/L. europaeus and L. europaeus/L. timidus and (ii) to assess the effects of climate change on each species as well as on their interspecific interactions. In their contact area L. granatensis achieved higher favourability values than L. europaeus, suggesting that if both species have a similar population status, the former species may have some advantages over the latter if competitive relationships are established. Climate change had the most striking effect on the distribution of L. timidus, especially when interspecific interactions with L. europaeus were taken into account, which may compromise the co-existence of L. timidus. The results of this study are relevant not only for understanding the distribution patterns of the hares studied and the effects of climate change on these patterns, but also for improving the general application of species distribution models to the prediction of the effects of climate change on biodiversity.