The main goal of this research is to develop one dimensional unsteady and nonequilibrium numerical sediment transport models for alluvial channels. Three mathematical and numerical models have been developed using kinematic, diffusion and dynamic wave approaches for simulating bed profiles in alluvial channels for unsteady and equilibrium conditions. Transient bed profiles were also simulated for several hypothetical cases, comparing different particle velocities and different particle fall velocities. Also different wave models (kinematic, diffusion and dynamic) were compared. The kinematic wave model was developed for simulating transient bed profiles in alluvial channels under unsteady and nonequilibrium conditions and tested with hypothetical data. The diffusion wave model was developed for simulating transient bed profiles in alluvial channels under unsteady, nonuniform and nonequilibrium conditions. It was found that the numerical comparison of kinematic, diffusion and dynamic wave for hypothetical cases of sediment transport revealed under the same sediment flux function of the wavefront is slower in the case of kinematic wave