In this paper, the surge and rotating stall post instability behaviors of anial flow compressors are investigated from a bifurcation-theoretic perspective. A sequence of local and global bifurcations of the nonlinear system dynamics is uncovered. This includes a previously unknown global bifurcation of a pair of large amplitude periodic solutions. Resulting from this bifurcation are a stable oscillation ("surge") and an unstable oscillation ("antisurge"). The latter oscillation is found to have a deciding significance regarding post-instability behavior experienced by the compressor. These results are used to reconstruct Greitzer's (1976) findings regarding the manner in which post-instability behavior depends on system parameters. Moreover, the results provide significant new insight deemed valuable in the prediction, analysis and control of stall instabilities in gas turbine jet engines.