Management of soil and water resources is one of the most critical environmental issues facing many countries. For that reason, dams, artificial channels and other water structures have been constructed. Management of these structures encounters fundamental problems: one of these problems is sediment transport.Theoretical and numerical modeling of sediment transport has been studied by many researchers. Several empirical formulations of transported suspended load, bed load and total load have been developed for uniform flow conditions. Equilibrium sediment transport under unsteady flow conditions has been just recently numerically studied. The main goal of this study is to develop one dimensional unsteady and nonequilibrium numerical sediment transport models for alluvial channels.Within the scope of this study, first mathematical models based on the kinematic, diffusion and dynamic wave approach are developed under unsteady and equilibrium flow conditions. The transient bed profiles in alluvial channels are simulated for several hypothetical cases involving different particle velocity and particle fall velocity formulations and sediment concentration characteristics. Three bed load formulations are compared under kinematic and diffusion wave models. Kinematic wave model was also successfully tested by laboratory flume data. Secondly, a mathematical model developed based on kinematic wave theory under unsteady and nonequilibrium conditions. The model satisfactorily simulated transient bed forms observed in laboratory experiments. Finally, nonuniform sediment transport model was developed under unsteady and nonequilibrium flow based on diffusion wave approach.The results implied that the sediment with mean particle diameter and the sediments with nonuniform particle diameters gave different solutions under unsteady flow conditions.