Experimental data for uranium adsorption on a complex weathered rock were simulated by twelve modelling teams from eight countries using surface complexation (SC) models. This intercomparison was part of an international project to evaluate the present capabilities and limitations of SC models in representing sorption by geologic materials. The models were assessed in terms of their predictive ability, data requirements, number of optimised parameters, ability to simulate diverse chemical conditions and transferability to other substrates. A particular aim was to compare the generalised composite (GC) and component additivity (CA) approaches for modelling sorption by complex substrates. Both types of SC models showed a promising capability to simulate sorption data obtained across a range of chemical conditions. However, the models incorporated a wide variety of assumptions, particularly in terms of input parameters such as site densities and surface site types. Furthermore, the methods used to extrapolate the model simulations to different weathered rock samples collected at the same field site tended to be unsatisfactory. The outcome of this modelling exercise provides an overview of the present status of adsorption modelling in the context of radionuclide migration as practised in a number of countries worldwide.