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Future flood and drought risks have been predicted to transition from moderate to high levels at global warmings of 1.5 °C and 2.0 °C above pre-industrial levels, respectively. However, these results were obtained by approximating the equilibrium climate using transient simulations with steadily warming. This approach was recently criticised due to the warmer global land temperature and higher mean precipitation intensities of the transient climate in comparison with the equilibrium climate. Therefore, it is unclear whether floods and droughts projected under a transient climate can be systematically substituted for those occurring in an equilibrated climate. Here, by employing a large ensemble of global hydrological models (HMs) forced by global climate models, we assess the validity of estimating flood and drought characteristics under equilibrium climates from transient simulations. Differences in flood characteristics under transient and equilibrium climates could be largely ascribed to natural variability, indicating that the floods derived from a transient climate reasonably approximate the floods expected in an equally warm, equilibrated climate. By contrast, significant differences in drought intensity between transient and equilibrium climates were detected over a larger global land area than expected from natural variability. Despite the large differences among HMs in representing the low streamflow regime, we found that the drought intensities occurring under a transient climate may not validly represent the intensities in an equally warm equilibrated climate for approximately 6.7% of the global land area.