This paper presents a method for developing control laws for nonlinear systems based on an optimal control formulation. Due to the nonlinearities of the system, no analytical solution exists. The method proposed here uses the 'black box' structure of a neural network to model a feedback control law. The network is trained with the back-propagation learning method by using examples of optimal control produced with a differential dynamic programming technique. Two different optimal control problems from flight control are studied. The produced control laws are simulated and the results analyzed. Neural networks show promise for application to optimal control problems with nonlinear systems.