This paper presents an adaptive backstepping neural controller (ABNC) to achieve precise rotor position tracking for a nonlinear active magnetic bearing (AMB) system with modeling uncertainties and external disturbances. In the proposed ABNC, the single-hidden layer feedforward networks (SLFNs) are used to approximate the unknown nonlinearities of dynamic systems and then based on the approximated models, the neural controller is constructed. Different from the existing methods, the hidden node parameters of the SLFNs are determined using the recently proposed neural algorithm named extreme learning machine (ELM), where these parameters are assigned randomly without adjusting. This simplifies the controller design process. Using the Lyapunov theory, stable tuning rules are derived for the update of the output weights of the SLFNs and a proof of stability in the uniformly bounded sense is given for the resulting controller. Moreover, to relax the online computation burden existing in the ABNC, a simplified ABNC (Simpl_ABNC) with less parameters to be adjusted online is proposed to improve the control performance. Finally the simulation results demonstrate that the proposed ABNC and Simpl_ABNC achieve better tracking performance comparing with other controllers including PID controller, conventional backstepping controller and adaptive backstepping sliding mode controller. Also the results show that the Simpl_ABNC has much less computation complexity and also better tracking performance than the ABNC. (C) 2015 Elsevier B.V. All rights reserved.