While compound weather and climate events (CEs) can lead to significant socioeconomic consequences, their response to climate change is mostly unexplored. We report the first multi-model assessment of future changes in return periods for the co-occurrence of heatwaves and drought, and extreme winds and precipitation based on the Coupled Model Intercomparison Project (CMIP6) and three emission scenarios. Extreme winds and precipitation CEs occur more frequently in many regions, particularly under higher emissions. Heatwaves and drought occur more frequently everywhere under all emission scenarios examined. For each CMIP6 model, we derive a skill score for simulating CEs. Models with higher skill in simulating historical CEs project smaller increases in the number of heatwaves and drought in Eurasia, but larger numbers of strong winds and heavy precipitation CEs everywhere for all emission scenarios. This result is partly masked if the whole CMIP6 ensemble is used, pointing to the considerable value in further improvements in climate models.