Issues concerning the global stabilization of axial compressors are presented. Instead of locally stabilizing the bifurcated rotating stall equilibria to avoid suddern performance drop, control schemes are proposed to globally stabilize the unstalled nominal operating points. These are achieved by employing nonlinear cancellation and backstepping designs via either throttle or direct mass flow rate control if the compressor characteristic satisfies the ‘left-tilt’ properly. The designs not only guarantee a safe operation close to the maximum achievable pressure rise, but the bifurcated system equilibria are also found to be stabilized due to the elimination of the jump phenomenon. Though both throttle and direct mass flow rate control schemes can be implemented for global stabilization, numerical simulations demonstrate that direct mass flow rate control achieves better post-stall system behaviour.