In this paper, input-output feedback linearization scheme is employed to stabilize the instabilities of axial flow compressor, specifically, for the so-called "surge"behavior . Two types of actuators are considered for the study. One is the throttle opening, and the other is the close-coupled valve. The axial flow compressors are found to be feedback linearizable via either of the two control inputs. Overall control law is then proposed to prevent the occurrence of the surge oscillation. Numerical results are also given to demonstrate the effectiveness of the proposed designs.