This thesis examines Artificial Neural Networks (ANNs) for rainfall-runoff modelling. A simple ANN was first developed to predict floods in the city of Rome, located in the Tiber River basin. A rigorous comparison of the ensemble ANN and the conceptual TEVERE model were undertaken for two recent flood events in 2005 and 2008. Both models performed well but the conceptual model was better at overall hydrograph prediction while the ANN performed better for the initial part of the event at longer lead times. Further experimentation with the ANN model was then undertaken to try to improve the model performance. Additional upstream stations and rainfall inputs were added including hourly totals, effective rainfall and cumulative rainfall. Different methods of normalisation and different ANN training algorithms were also implemented along with four alternative methods for combining the ensemble ANN predictions. The results showed that the ANN was able to extrapolate to the 2008 event. Finally, Empirical Mode Decomposition was applied to the ANN to examine whether this method has value for ANN rainfall-runoff modelling. At the same time the impact of the random initialisation of the weights of the ANN was investigated for the Potomac River and Clark Fork River catchments in the USA. The EMD was shown to be a valuable tool in detecting signal properties but application to ANN rainfall-runoff modelling was dependent on the nature of the dataset. Overall uncertainty from the random initialisation of weights varied by catchment where uncertainties were shown to be very large at high stream flows. Finally, a suite of redundant and non-redundant model performance measures were applied consistently to all models. The value of applying a range of redundant and non-redundant measures, as well as benchmark-based methods was demonstrated.