This paper presents an adaptive parallel processing control scheme, using an artificial neural network (ANN) which is trained while the controller is operating on-line. The proposed control structure incorporates five-multilayer feedforward ANNs, which are on-line, trained, using the Levenburg-Marquadt learning method. The five networks are used exclusively for system estimation. The estimation mechanism uses continual on-line training to learn the unknown stator model dynamics and estimate the rotor fluxes of an inverter-fed induction motor. Subsequently, the estimated stator currents are fed into an adaptive controller to track the desired stator current trajectories. The adaptive controller is constructed as a feedback signal (a predetermined control law), depending on estimated stator currents supplied by the neural estimators and the reference trajectories to be tracked by the output. The control of the direct and quadrature components of the stator current successfully tracked a wide variety of reference trajectories after relatively short, on-line training periods. This paper also suggests two three-layer ANNs control scheme to simultaneously identify and adaptively adjust the rotor speed to follow a predetermined reference track.