•Structured patterns of primary succession were observed under rapid warming in the alpine tropics.•Wind-dispersed species were overrepresented whereas nurse plants were poorly effective.•Poor facilitative effects are the result of insufficient time for nurses to establish and grow.•The time lag between warming and plant migration generates altered alpine communities. Species range shifts and possible species extinctions in alpine regions are hypothesized being influenced by the increasing time lag between the velocity of global warming and the slowness of primary succession. We tested this hypothesis in tropical alpine environments above 4700 m a.s.l. (Central Andes) and we explored the underlying mechanisms at work by using four sites gradually deglaciated since the acceleration of warming in the late 1970’s. These post-glacial chronosequences, made available by a multidisciplinary approach combining glaciology and ecology, are extremely rare and provide a pertinent space-for-time substitution for the study of climate change effects. We found consistent patterns in plant succession (abundance, species richness and functional strategies) along the four chronosequences. Dispersal limitation was a prominent constraint for succession, even at the end of the chronosequences, leading to an overrepresentation of anemochorous species in comparison with adjacent ecosystems. Nurse plants were infrequent and their low maturity seemed to make them poorly efficient as facilitators, contrarily to the expectations made by the stress-gradient hypothesis in alpine regions. This suggests that, despite the accelerating rate of warming, the dynamics of primary succession remains slow, generating a climatic debt and hampering the adaptation to climate change in alpine plant communities.