Quantitative estimates of the range loss of mountain plants under climate change have so far mostly relied on static geographical projections of species' habitat shifts(1-3). Here, we use a hybrid model(4) that combines such projections with simulations of demography and seed dispersal to forecast the climate-driven spatio-temporal dynamics of 150 high-mountain plant species across the European Alps. This model predicts average range size reductions of 44-50% by the end of the twenty-first century, which is similar to projections from the most 'optimistic' static model (49%). However, the hybrid model also indicates that population dynamics will lag behind climatic trends and that an average of 40% of the range still occupied at the end of the twenty-first century will have become climatically unsuitable for the respective species, creating an extinction debt(5,6). Alarmingly, species endemic to the Alps seem to face the highest range losses. These results caution against optimistic conclusions from moderate range size reductions observed during the twenty-first century as they are likely to belie more severe longer-term effects of climate warming on mountain plants.