Models of fluvial bedload sediment transport have been developed at two scales: individual particle movement and mass transport of sediment. The model of the movement of individual sediment particles includes the stochastic influences due to the flow and the structure of the bed. This model was used to calculate distributions of particle movement. These were then used to calculate sediment transport over a mobile bed including the effects of the stochastic influences on particle movement. The model of individual sediment particle movement includes descriptions of initiation of motion, rolling, non-contact motion and impact. The movements of sediment particles are calculated under the influence of turbulent velocity fluctuations, using a particle tracking method. Movements of initially coincident fluid and sediment particles are calculated, fluid movement due to mean flow and velocity fluctuations, sediment particle movement due to the fluid. The influence of fluid on sediment is continued until no correlation remains, either due to the separation of fluid and sediment or to elapsed time. At this point new conditions for the fluid are calculated. Observations of particle movements in sediment transport show a range of particle movements for the same conditions, due to the stochastic influences of the structure of the bed and the turbulent flow. The particle model was used to calculate distributions of particle movements by repeated calculations of particle tracks on a parallel processing computer. These distributions were used to describe the behaviour of particles, fraction entrained, time in motion and distance travelled. The distributions were used to calculate the rate of sediment transport and the effects of sediment transport over a mobile bed. Their use in these calculations allowed the influence of stochastic processes at the scale of individual particle movements to influence the calculated sediment transport.