Abstract: In discussing the basic charact eristics of the perturbation equations set which describes the generalized geost rophic currentst ability of the two -dimensional adiabatic and non-dispersive symmetry at mosphere, it is obtained that the system with these charac-teristics can be described by the unified form equations set. According to this, the following results are demonstrated:(1) the solutions of the unified for mequations set exist;(2) the charact eristics of the groundstate are decided by:a. groundst ate is stable, when + min(G) > 0; b. groundstate is unstable, when +min(G) < 0;(3) the global stability of groundst ate can be given interms of the local one;(4) the result are effective which are obtained from reasonable and sufficient simplified analysis of local stability.