Abstract. Projections of changes in the hydrological cycle from global hydrological models (GHMs) driven by global climate models (GCMs) are critical for understanding future occurrence of hydrological extremes. However, uncertainties remain large and need to be better assessed. In particular, recent studies have pointed to a considerable contribution of GHMs that can equal or outweigh the contribution of GCMs to uncertainty in hydrological projections. Using six GHMs and five GCMs from the ISI-MIP multi-model ensemble, this study aims: (i) to assess future changes in the frequency of both high and low flows at the global scale using control and future (RCP8.5) simulations by the 2080s, and (ii) to quantify, for both ends of the runoff spectrum, GCMs and GHMs contributions to uncertainty using a two-way ANOVA. Increases are found in high flows for northern latitudes and in low flows for several hotspots. Globally, the largest source of uncertainty is associated with GCMs, but GHMs are the greatest source in snow-dominated regions. More specifically, results vary depending on the runoff metric, the temporal (annual and seasonal) and regional scale of analysis. For instance, uncertainty contribution from GHMs is higher for low flows than it is for high flows, partly owing to the different processes driving the onset of the two phenomena (e.g. the more direct effect of the GCMs' precipitation variability on high flows). This study provides a comprehensive synthesis of where future hydrological extremes are projected to increase and where the ensemble spread is owed to either GCMs or GHMs. Finally, our results underline the need for improvements in modelling snowmelt and runoff processes to project future hydrological extremes and the importance of using multiple GCMs and GHMs to encompass the uncertainty range provided by these two sources.