This thesis examines the potential role of transfer function models in the real-time forecasting of the rainfall-runoff and flow routing processes. The theory of the transfer function model structure and the recursive least-squares estimator is described. The use of a sampling rule to reduce the order of large transfer function models is discussed. Traditional sampling theories and control engineering sampling rules are examined. An hydrological sampling rule is developed and tested, with the conclusion that accurate and parsimonious transfer function models can be calibrated for most of the hydrological systems considered in this thesis. Accepted methods of flow routing and river-basin modelling are introduced. Synthetic simulations of the flow routing process by transfer function models are compared to linear and non-linear, hydrological and hydraulic methods of flow routing. The transfer function model structure adequately simulates simple and more complex synthetic systems which exhibit tributary inflow, varying roughness parameters and out-of-bank flooding. A sampled cascade model structure is developed as an alternative model order reduction technique. Use is made of the Rosenbrock parameter optimisation method. The transfer function model structure is used to forecast flows in three case studies. The first two applications concentrate on the ability of transfer function models to approximate tributary inflows and the use of a dual-model structure to simulate out-of-bank flooding. Finally, an accurate and parsimonious river-basin model structure is proposed for the real-time forecasting of flows in river catchments