Layered neural networks are used in a nonlinear adaptive tracking problem. The plant is an unknown feedback-linearizable discrete-time system, represented by an input-output model with relative degree higher than one. A state space model of the plant is obtained to define the zero dynamics, which are assumed to be stable. Layered neural networks are used to model the plant and generate controls. Some error between the model and the plant is allowed. A dead-zone is specified in the updating rule. A local convergence result is given.