The higher order Galerkin expansion of the Moore-Greitzer model of instabilities in compression systems was proposed. The identification of stability was conducted based on this model. The conditions of emergence of rotating stall and surge were concluded qualitatively. Stall only depends on the throttle parameter

but surge depends on both of throttle parameter and stability parameter. Then dynamic behavior was piecewise investigated from axisymmetric steady flow to surge with a cubic compressor characteristic. Simulation results show that the higher-order disturbance velocity potential harmonics strongly interact with the first harmonic during stall inception. Forming stall behavior from axisymmetric steady flow in higher-order model is faster by about sixteen percent than in first order model. Thus the occurrence of unstable phenomena at the onset is earlier. Initial disturbance is more sensitive to the higher order model.