Abstract: It is mathematically and thoroughly proved in this paper that the nonli near stochastic ocean atmosphere oscillator model possesses a stable limit cycle;then the model equations are transformed into the FokkerPlanck equation (FPE ),and the evolution of El Ni oSouthern Oscillation (ENSO) from unstab le state t o stable state is studied from the point of view of nonequilibrium system dynami cs for the first time. The system evolution from an initially unstable state to asteady state has been studied in this paper in terms of FPE expansion theory,and under the dominance of the most unstable manifold the system evolves towards only to a pair of symmetric steady states: one is considered as quasinormal climatic state, and the other as anomalous climatic state, i.e. strong ENSO state.This study indicates that even if the initial distribution is not at the origin state, known from the deterministic equations the system will evolve towards an tisymmetric steady states, however under the effect of stochastic forcing, the system exhibits intrinsic differences from deterministic systems,i.e. when t →∞ , the overwhelming majority probability still distributes halfandhalf in a p air of symmetric potential wells, and there is almost no probability distribution in a pair of antisymmetric potential wells. This is in consistent with observati onal facts. Viewed from dynamic macro theory, quasi normal climate state and strong ENSO state are two equilibrium states, follows an unified dynamic theoretica l framework, and have the same temporal/spatial scales; ENSO is a joint name of Southern Oscillations and El Ni o cycles and bring them into an unified framewor k system in study is reasonable. However viewed from dynamic microtheory, Sout h ern Oscillations, El Ni o and La Nina reflect different phases of Climat e, in or der to reflect the phase transition between El Ni o and La Nina, it is necessary to establish their dynamic frameworks respectively.