Stability conditions for a parallel dynamic neural network by means of Lyapunov-like analysis are determined. The new learning law ensures that the identification error converges to zero (model matching) or to a bounded zone (with unmodelled dynamics). Based on the neural identifier we present a local optimal controller and analyse the tracking error. Our principal contributions are that we provide a bound for the identification error of the parallel neuro identifier and that we then establish a bound for the tracking error of the neurocontrol.