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In recognition of the non-linear relationship between storage and discharge existing in most river systems, non-linear forms of the Muskingum model have been proposed, together with methods to calibrate the model parameters. However, most studies have focused only on routing a typical hypothetical flood hydrograph characterized by a single peak. In this study, we demonstrate that the storage-discharge relationship adopted for the non-linear Muskingum model is not adequate for routing flood hydrographs in natural channels, which are often characterized by multiple peaks. As an alternative, an evolutionary algorithm-based modelling approach, i.e. genetic programming (GP), is proposed, which is found to route complex flood hydrographs accurately. The proposed method is applied for constructing a routing model for a channel reach along the Walla Walla River, USA. The GP model performs extremely well with a root-mean-square error (RMSE) of 0.73 m3 s-1 as against an RMSE of 3.26 m3 s-1 for routing the multi-peaked hydrograph. The advantage of GP lies in the fact that, unlike other models, it establishes the routing relationship in an easy and simple mathematical form. Copyright © 2007 John Wiley & Sons, Ltd.