The derivation of a generalized, non-linear, diffusion wave equation, which explicitly includes inertial effects, is presented. The generalized equation is an approximation to the Saint-Venant equations of order epsilon, where epsilon is a characteristic ratio of the water surface slope to the bed slope. The derivations are carried out using a general expression for how resistance, representing both friction and form drag. Some simplified forms of the generalized diffusion wave equation, useful for different practical applications, are given, A numerical finite difference model, solving a particular simplified form of the generalized equation, is used to simulate a number of observed floods in a natural river reach, The model is then used to investigate the effects of non-linearity on the characteristics of flood wave propagation. (C) 1997 Elsevier Science B.V.