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 model⁴ 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.