The frequency of heatwaves, droughts and their co-occurrence vary greatly in simulations of different climate models. Since these extremes are expected to become more frequent with climate change, it is important to understand how vegetation models respond to different climatologies in heatwave and drought occurrence. In previous work, six climate scenarios featuring different drought-heat signatures have been developed to investigate how single versus compound extremes affect vegetation and carbon dynamics. Here, we use these scenarios to force six dynamic global vegetation models to investigate model agreement in vegetation and carbon cycle response to these scenarios. We find that global responses to different drought-heat signatures vary considerably across models. Models agree that frequent compound hot-dry events lead to a reduction in tree cover and vegetation carbon stocks. However, models show opposite responses in vegetation changes for the scenario with no extremes. We find a strong relationship between the frequency of concurrent hot-dry conditions and the total carbon pool, suggesting a reduction of the natural land carbon sink for increasing occurrence of hot-dry events. The effect of frequent compound hot and dry extremes is larger than the sum of the effects when only one extreme occurs, highlighting the importance of studying compound events. Our results demonstrate that uncertainties in the representation of compound hot-dry event occurrence in climate models propagate to uncertainties in the simulation of vegetation distribution and carbon pools. Therefore, to reduce uncertainties in future carbon cycle projections, the representation of compound events in climate models needs to be improved.