The process basis of existing soil-erosion models is shown to be ill-founded. The existing literature builds directly or indirectly on Bennett's (1974) paper, which provided a blueprint for integrated catchment-scale erosion modelling. Whereas Bennett recognized the inherent assumptions of the approach suggested, subsequent readings of the paper have led to a less critical approach. Most notably, the assumption that sediment movement could be approximated by a continuity equation that related to transport in suspension has produced a series of submodels that assume that all movement occurs in suspension. For commonly occurring conditions on hillslopes, this case is demonstrably untrue both on theoretical grounds and from empirical observations. Elsewhere in the catchment system, it is only partially true, and the extent to which the assumption is reasonable varies both spatially and temporally. A second ground-breaking paper -that of Foster and Meyer (1972) -was responsible for subsequent uncritical application of a first-order approximation to deposition based on steady-state analysis and again a weak empirical basis. We describe in this paper an alternative model (MAHLERAN -Model for Assessing Hillslope-Landscape Erosion, Runoff And Nutrients) based upon particle-travel distance that overcomes existing limitations by incorporating parameterizations of the different detachment and transport mechanisms that occur in water erosion in hillslopes and small catchments. In the second paper in the series, we consider the sensitivity and general behaviour of MAHLERAN, and test it in relation to data from a large rainfall-simulation experiment. The third paper of the sequence evaluates the model using data from plots of different sizes in monitored rainfall events. From this evaluation, we consider the scaling characteristics of the current form of MAHLERAN and suggest that integrated modelling, laboratory and field approaches are required in order to advance the state of the art in soil-erosion modelling. Wainwright et al., 2001;Parsons et al., 2004Parsons et al., , 2006b. We have argued elsewhere (Parsons et al., 2004) that these problems arise from a fundamental misconception, and thus misrepresentation, of the component processes that make up soil erosion. The aim of this paper is, therefore, to review the conceptual basis of existing models and to propose an alternative model that addresses the problems inherent in existing approaches. Figure 2. Comparison of information on (a) travel distances and (b) virtual velocities from Hassan et al. (1992) for concentrated flows and Parsons et al. (1998) for unconcentrated flows. See the text for further discussion.822 J. Wainwright et al.Figure 4. Summary of the calculation algorithm used in MAHLERAN. The main components in terms of detachment and the use of travel distance and virtual velocity to estimate sediment discharge are highlighted. 824 J. Wainwright et al.appropriate erosion and deposition rates have been calculated. The sediment mass-balance Equation (6) is equiva...