The non-linear behaviour of catchments, as ascertained by various investigators, is discussed. Blackbox analysis with Laguerre functions shows non-linear behaviour for a small urban catchment area. Some approaches to non-linear systems for rainfall and run-off are considered. Two quasilinear methods are compared with a theoretical model for their application. Results from an application of the most promising method on an urban catchment area confirm the feasibility of this method. Six conceptual models are compared and an application of the quasilinear method is given with a conceptual model. A satisfactory treatment of losses forms a major problem in modelling urban rainfall and run-off. Hence a chapter is devoted to transformation of rainfall into sewer inflow and concurrent losses. The use of critical sequences of rainfall for modelling is discussed. Evidence suggesting the maximum time interval between samples is given.