This paper discusses the nonlinear control of surge in axial compression systems. A nonlinear model-based Luenberger-type observer is first developed from a simple incompressible flow model of an axial compressor rig; then the input-output feedback Linearizing control technique is employed to derive an appropriate control law. The use of the output observer as the basis for the control design enables the reconstruction of approximate system states from a single output measurement, it enhances transient tracking of measured output, and it reduces the destabilizing effect of measurement noise in closed loop. The nonlinear controller described in this work achieves an implicit linearization of the dynamics between the measured output variable, the dynamic pressure at the compressor inlet and the system input variable (the throttle area parameter). The designed controller is validated by both simulation and experimental demonstration on an axial compressor experimental rig. The controlled system responses show adequate stabilization of the surge dynamics in the presence of impulsive persistent disturbances in system conditions. Further evaluation of the overall controlled system performance is enhanced by comparisons with a linear surge controller. It is shown that gain scheduling along nominal conditions is not required to maintain uniform closed-loop performance, during tracking of setpoint changes, with the nonlinear controller.