Phenological changes are well documented biological effects of current climate change but their adaptive value and demographic consequences are poorly known. Game theoretical models have shown that deviating from the fitness-maximising phenology can be evolutionary stable under frequency-dependent selection. We study eco-evolutionary responses to climate change when the historical phenology is mismatched in this way. For illustration we model adaptation of arrival dates in migratory birds that compete for territories at their breeding grounds. We simulate climate change by shifting the timing and the length of the favourable season for breeding. We show that initial trends in changes of population densities can be either reinforced or counteracted during the ensuing evolutionary adaptation. We find in total seven qualitatively different population trajectories during the transition to a new evolutionary equilibrium. This surprising diversity of eco-evolutionary responses provides adaptive explanations to the observed variation in phenological responses to recent climate change.