This paper considers the problem of distributed control of dynamically coupled nonlinear systems that are subject to decoupled constraints. Examples of such systems include certain large scale process control systems, chains of coupled oscillators and supply chain management systems. Receding horizon control (RHC) is a method of choice in these venues as constraints can be explicitly accommodated. In addition, a distributed control approach is sought to enable the autonomy of the individual subsystems and reduce the computational burden of centralized implementations. In this paper, a distributed RHC algorithm is presented for dynamically coupled nonlinear systems that are subject to decoupled input constraints. By this algorithm, each subsystem computes its own control locally. Provided an initially feasible solution can be found, subsequent feasibility of the algorithm is guaranteed at every update, and asymptotic stabilization is established. The theoretical conditions for feasibility and stability are shown to be satisfied for a set of coupled Van der Pol oscillators that model a walking robot experiment. In simulations, distributed and centralized receding horizon controllers are employed for stabilization of the oscillators. The numerical experiments show that the controllers perform comparably, while the computational savings of the distributed implementation over the centralized implementation is clearly demonstrated.