In this paper the control of formations of multiple nonholonomic mobile robots is attempted by integrating a kinematic controller with a neural network (NN) computed-torque controller. A combined kinematic/torque control law is developed for leader-follower based formation control using backstepping in order to accommodate the dynamics of the robots and the formation in contrast with kinematic-based formation controllers. The NN is introduced to approximate the dynamics of the follower as well as its leader using online weight tuning. It is shown using Lyapunov theory that the errors for the entire formation are uniformly ultimately bounded, and numerical results are provided.