I propose that global patterns in numbers of range–restricted endemic species are caused by variation in the amplitude of climatic change occurring on time–scales of 10–100 thousand years (Milankovitch oscillations). The smaller the climatic shifts, the more probable it is that palaeoendemics survive and that diverging gene pools persist without going extinct or merging, favouring the evolution of neoendemics. Using the change in mean annual temperature since the last glacial maximum, estimated from global circulation models, I show that the higher the temperature change in an area, the fewer endemic species of mammals, birds, reptiles, amphibians and vascular plants it harbours. This relationship was robust to variation in area (for areas greater than 104 km2), latitudinal position, extent of former glaciation and whether or not areas are oceanic islands. Past climatic change was a better predictor of endemism than annual temperature range in all phylads except amphibians, suggesting that Rapoport' rule (i.e. species range sizes increase with latitude) is best explained by the increase in the amplitude of climatic oscillations towards the poles. Globally, endemic–rich areas are predicted to warm less in response to greenhouse–gas emissions, but the predicted warming would cause many habitats to disappear regionally, leading to species extinctions.