Layered neural networks are used in a nonlinear self-tuning adaptive control problem. The plant is an unknown feedback-linearizable discrete-time system, represented by an input-output model, with a relative degree possibly higher than one. To arrive at a convergence result, a dead zone is used in the neural network updating rule. The result indicates that for any initial conditions of the plant, if the neural network model contains a sufficient number of nonlinear hidden neurons and if the initial guess of the network weights is sufficiently close to the correct weights, then the tracking error between the plant output and the reference command will converge to a bounded ball. Computer simulations verified the theoretical result.