Aerodynamic instabilities due to rotating stall initiation and surge trigger in the axial flow compressors were investigated using different mathematical models. Limit of stability of the rotating stall was detected using simple model that considers transport of energy by the rotor wakes passing through the stator. Active suppression of the aerodynamic instabilities in the axial flow compressors were demonstrated using mechanical compensated system with controlled plenum simultaneously with air injection through reed valve. A nonlinear controller based on a bifurcation theory was used to design feedback control system for eliminating surge and rotating stall as well hysteresis. The bifurcation analysis was performed to determine the effect of throttle gain on the compressor limit of stability and then modifying the throttle characteristic to eliminate hysteresis and suppresses surge. The Moore–Greitzer model was extended to include the influences of the air injection on the axial flow compressors performance characteristics and to enhance the limit of stabilities of both the stall and the surge. Comparisons of the present theoretical results with the available previous experimental and theoretical results were carried out.