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Although global- and catchment-scale hydrological models are often shown to accurately simulate long-term runoff time-series, far less is known about their suitability for capturing hydrological extremes, such as droughts. Here we evaluated simulations of hydrological droughts from nine catchment scale hydrological models (CHMs) and eight global scale hydrological models (GHMs) for eight large catchments: Upper Amazon, Lena, Upper Mississippi, Upper Niger, Rhine, Tagus, Upper Yangtze and Upper Yellow. The simulations were conducted within the framework of phase 2a of the Inter-Sectoral Impact Model Intercomparison Project (ISIMIP2a). We evaluated the ability of the CHMs, GHMs and their respective ensemble means (Ens-CHM and Ens-GHM) to simulate observed hydrological droughts of at least one month duration, over 31 years (1971–2001). Hydrological drought events were identified from runoff-deficits and the Standardised Runoff Index (SRI). In all catchments, the CHMs performed relatively better than the GHMs, for simulating monthly runoff-deficits. The number of drought events identified under different drought categories (i.e. SRI values of -1 to -1.49, -1.5 to -1.99, and ≤-2) varied significantly between models. All the models, as well as the two ensemble means, have limited abilities to accurately simulate drought events in all eight catchments, in terms of their occurrence and magnitude. Overall, there are opportunities to improve both CHMs and GHMs for better characterisation of hydrological droughts.