A dynamic model and differential equation of asymmetric dual-discs overhanging rotor system were established,taking into account the casing elasticity, rotary dynamic excitation of bearings, elastic connection between casing and stator, and gyroscopic effect. Based on the theory of stability, the system stability and the stability regions were studied by unvestigating theproperties of the jacibu matrix. The effects of different parameters on stability regions of the system were discussed. The step response curves and zero-pole map were utilized for identification of system stability quickly and directly. The results show that rotary dynamic excitation of bearing and rub-impact go against stable operation of the system; The influences of stiffness of the two bearings on stability are basically the same. The influence of the excitation of the two bearings and the rub-impact of the two discs on stability is different obviously. The smaller the elastic connection stiffness between casing and casing is, and the bigger the elastic connection stiffness between casing and stator is, the better the system stability is. When the stiffness is bigger than the critical bearings stiffness, there appearstability regions in the system; otherwise, there are no such regions.