Future projections of low flows are associated with different types of uncertainties, due to an imperfect knowledge of both future climate and rainfall-runoff processes. Due to computational constraints, impact and adaptation studies unfortunately cannot always afford to perform a detailed analysis of all these uncertainties. In that case, the modelling efforts have to focus on the most relevant source of uncertainty in order to provide the best estimate of the overall uncertainty. The present study thus aims at assessing the hierarchy of uncertainties in changes on low flows at the scale of France, within the national Explore2070 project. Amongst all possible sources of uncertainties, two are here considered: (1) the uncertainty in General Circulation Model (GCM) configuration, with 7 different models that adequately sample the range of changes as projected by the GCMs used in the IPCC AR4 over France, and (2) the uncertainty in hydrological model structure, with 2 quite different models: GR4J, a lumped conceptual model calibrated on each target catchment, and Isba-Modcou, a suite of a land surface scheme and a distributed hydrogeological model not fully calibrated at the catchment scale. The hydrological models have been run at more than 1500 locations in France over the 1961-1990 baseline period with forcings from both the Safran near-surface atmospheric reanalysis and the GCM control runs statistically downscaled with a weather type method, and over the 2046-2065 period with forcings from all downscaled GCM runs under the A1B emissions scenario. Various low-flow indices have been computed for both periods: the annual minimum monthly flow with a 5-year return period (QMNA5, commonly used as a policy threshold in France), the annual minimum 10-day mean flow with a 2-year return period (VCN10-2), the daily flow value exceeded 95% of the time (Q95), as well as a seasonality index. All low-flow indices show a dramatic increase in drought severity for the mid 21st century, with large uncertainties due to both future climate and associated hydrological response. An analysis of variance has been performed for each low-flow index and at all stations shared by the two hydrological models (around 550) in order to assess the two considered sources of uncertainty and their hierarchy. Results first show spatial differences over France in the amount of overall uncertainty due to both sub-regional climate change patterns and catchment properties. The analysis of hierarchy between climate and hydrological uncertainties shows a large spread over France for any single low-flow index, with the uncertainty in hydrological response appearing as important as the uncertainty in future climate. The large uncertainty in hydrological modelling partly comes from the difference in the way the two models simulate low flows and the way they are calibrated, which results in significant differences in their efficiency in low-flow simulation in the baseline period. The results of this study will help to define the relevant hydrological scenarios to be used in the adaptation part of the Explore2070 project for deriving national-scale adaptation strategies.