Dynamic compressors are susceptible to aerodynamic instabilities while operating at low mass flow rates. These instabilities, rotating stall and surge, are detrimental to engine life and operational safety, and are thus undesirable. In order to prevent stability problems, a passive technique, involving fuel flow scheduling, is currently employed on gas turbines. The passive nature of this technique necessitates conservative stability margins, compromising performance and/or efficiency. In the past, model based active control has been proposed to enable reduction of margin requirements. However, available compressor stability models do not predict the different stall inception patterns, making model based control techniques practically infeasible. This research presents active stability management as a viable alternative. In particular, a limit detection and avoidance approach has been used to maintain the system free of instabilities. Simulations show significant improvements in the dynamic response of a gas turbine engine with this approach. A novel technique has been developed to enable real-time detection of stability limits in axial compressors. It employs a correlation measure to quantify the chaos in the rotor tip region. Analysis of data from four axial compressors shows that the value of the correlation measure decreases as compressor loading is increased. Moreover, sharp drops in this measure have been found to be relevant for stability limit detection. The significance of these drops can be captured by tracking events generated by the downward crossing of a selected threshold level. It has been observed that the average number of events increases as the stability limit is approached in all the compressors studied. These events appear to be randomly distributed in time. A stochastic model for the time between consecutive events has been developed and incorporated in an engine simulation. The simulation has been used to highlight the importance of the threshold level tosuccessful stability management. The compressor stability management concepts have also been experimentally demonstrated on a laboratory axial compressor rig. The fundamental nature of correlation measure has opened avenues for its application besides limit detection. The applications presented include stage load matching in a multi-stage compressor and monitoring the aerodynamic health of rotor blades.