Hydrological model calibration should consider two different concepts of predictive uncertainty referring respectively to the statistical uncertainty and the so-called multi-objective equivalence. Currently available studies present different methods to quantify the statistical uncertainty inherent in the calibrated model parameters and the modelling error. The multi-objective equivalence of several parameter sets or model structures has been pointed out in many studies and several methods exist to identify these equivalent solutions. Two main questions are however still not answered: How can the multi-objective equivalence be translated into a proper prediction uncertainty? And how can the two sources of uncertainty be integrated into a total predictive uncertainty? The present work illustrates this problem based on a case study in the Swiss Alps, a high mountainous catchment used for hydropower production. The discharge from this water resources system is simulated through a conceptual semi-lumped model. A Bayesian inference method – the so-called Metropolis-Hastings algorithm – is used to quantify the parameter uncertainty and the overall modelling error for a given model structure. Different equivalent model structures are identified through a multi-objective evolutionary algorithm that enables the joint optimisation of the model structure and the model parameters. A method is presented to estimate the prediction uncertainty resulting form these multi-objective equivalent model structures and the resulting model output distribution is compared to the statistical uncertainty.