A numerical model, which simulates the dynamics of alluvial river channels on geological (Quaternary) time scales, is presented. The model includes water flow, channel dimensions, sediment transport and channel planform type. A number of numerical experiments, which investigate the response of an alluvial river to imposed sequences of water and sediment supply, with special emphasis on the time lags between these controlling variables, as well as a downstream discharge increase, are presented. It is found that the influence of the time lags can be substantial, having major implications for the reconstructions of palaeo climate based on river channel behavior documented in the geological record. The model is further applied to both a conceptual warm - cold - warm cycle and a reconstructed evolution of the river Meuse, the Netherlands, during the Late Glacial-Holocene warming. Results show that the model is capable of explaining the response of this river, although better validation against palaeoenvironmental data remains necessary. © 2000 Elsevier Science B.V.