Based on the theory developed by Moore and Greitzer, a new simplifying approximation, which takes into account the influence of higher harmonics of rotating waves, is proposed in this paper to get a simplified model of post stall transients in axial compression systems. This approximation leads to a set of three simultaneous nonlinear first order partial differential equations. The further investigation of post stall behavior for different response modes of instabilities (rotating stall and/or surge), recoverability, prestall period during stall inception, and the effect of compression system parameters on them can be carried out by this model and has been discussed in detail in the present paper. It has been found that stall inception exhibits a large prestall period in the region with small slope of compressor characteristic, and in this region, final throttle setting, compressor characteristic and time-lag parameters have a strong influence on the period. The inertia parameters of blade rows have a strong influence on the recoverability of compression systems and the blockage of stall cell at recovery point. Some qualitative comparisons with available experimental results and experience are made, and it shows that the proposed model is very simple and reliable. It is well known, t h a t the useful o p e r a t i n g range of t u r b o m a c h i n e r y compression systems is limited by the onset of one of the two kinds of fluid d y n a m i c instabilities: r o t a t i n g stall a n d surge, a n d b o t h of t h e m will degrade compression s y s t e m performance and d u r a b i l i t y [1]. These two kinds of instabilities, however, have some basic distinct characteristics. For instance, when r o t a t i n g stall occurs in the compres-Received, 1999. sion system, it is very difficult to r e t u r n to an unstalled s i t u a t i o n because of the hysteresis, a n d if the system enters the nonrecoverable stall, the only remedy m a y be to shut down the system and r e s t a r t it [2]. But it is not very difficult to recover from surge to a stable o p e r a t i o n by opening the t h r o t t l e again. Therefore, the p r o b l e m of post stall transients, the recovery process from stalled flow, and the influence of syst e m p a r a m e t e r s in a compression system have been concerned a b o u t by aircraft engine researchers and designers[3~15].