l model whithout this restriction this has been done by taking more grain fractions into consideration. (Model for non - uniform or graded sediment). This extension of the mathematical model for uniform sediment is described in chapter 1, where the basic equations of the model for uniform as well as for non - uniform sediment are derived. The main assumptions in the deductions are that the flow can be considered quasi - steady and that the sediment transport is a function of the local hydraulic conditions. The characteristic directions in the model for non - uniform sediment are derived, in case of two grain fractions, and will be briefly analysed. In chapter 2 the basic equations will be discussed and some models for the component parts of the mathematical models will be suggested. Here also some of the general limitations for the morphological computation will be mentioned. An extensive numerical analysis of some finite difference methods for a linear hyperbolic equation is given in chapter 3. A predictor - corrector method is preferred for the solution of the model for non - uniform sediment, and the method is tested on the model for uniform sediment in order to check the applicability to a non -linear hyperbolic system. Finally the predictor - corrector method will be applied to the model for non - uniform sediment after a schematization of the vertical grain size distribution is carried out. The computational results from the numerical model for nonuniform sediment will be compared with solutions obtained from the characteristic method.