Gullies in the Guadalentin catchment, SE Spain, are formed in a variety of lithologies, ranging from schists to marls. There are clear differences in valley and channel morphology between these two types. Gully erosion in schists produces large amounts of clastic material that restricts sediment transport, leading to a relatively smooth transition from gullies to hillslopes, and to broad alluvial valley bottoms with laterally migrating channels. Gullies in marls contain only limited gravels, so gully extension leads to sharply incised gully heads. A two-dimensional model has been developed to investigate and simulate the distribution of gully heads in the Guadalentin. The model runs on a smooth initial surface with an added fractal perturbation. Without some perturbation of the initial surface or material properties, symmetry prevents the formation of any channels. Fractal perturbation was used here to provide initial irregularities at all scales. This paper explores the dependence of model response on the form of the sediment transport law. Initially, sediment transport was considered to be transport-limited and so depends oh the relationship between wash and creep/splash. This was modified by (i) altering the exponents for gradient and area to conform with experimental results, (ii) adding a critical tractive power for the initiation of rillwash, (iii) including a more explicit treatment of mass movements, (iv) including terms to reduce the dependence of the model on the computational grid size, (v) providing a basis for explicitly integrating from individual storms to average long-term behaviour and, most critically (vi) introducing the 'effective bedload fraction' (ebf) as a simplifying concept to allow for the selective transportation of eroded sediment. This modification allows the model to represent removal of fines in marl-rich catchments, without the need to introduce a fully explicit travel distance formulation. The steep gully heads and vertical side walls developed in marl catchments in the Guadalentin basin are qualitatively well-represented by the model. Preliminary tests showed that steep-walled gullies are generated where the ebf falls to below about 0.5. If a tractive power threshold is also introduced, gentler headcuts are produced. Selective transportation is thus seen as the critical determinant of steep headcuts in gully systems. (C) 2000 Elsevier Science B.V.