The transport of sand by wind results from the equilibrium between the erosion of grains dragged by the flow and the resulting slow down of the wind velocity. The dynamical mechanisms governing the saturation of the sand flux are investigated theoretically. We first demonstrate that previous models, based on the assumption that all the grains have the same trajectory, are either not self-consistent or lead to unstable solutions. A model based on a discrete number of states is derived, which solves these problems. Two well-defined species of grain appear, which correspond to saltons (high-energy grains) and reptons (grains ejected from the sand bed by the impact of saltons). They play specific roles: the negative feedback of the transport on the wind is limited to the reptation layer while most of the transport is due to saltation. The model is further simplified, benefiting from the existence of these two species and the dependencies of the threshold velocity, the saturated flux, the aerodynamic roughness and the saturation length are derived and compared to experimental measurements.