It is mathematically and thoroughly proved in this paper that the nonlinear stochastic ocean-atmosphereoscillator model possesses a stable limit cycle; then the model equations are transformed into the Fokker-Planck equation (FPE), and the evolution of El Ni?o-Southern Oscillation (ENSO) from unstable state tostable state is studied from the point of view of nonequilibrium system dynamics. The study results revealthat although the complex nonlinear ocean-atmosphere oscillator model possesses multiequilibrium states,the real climatic system possesses only a quasi-normal state and a strong ENSO cycle stable state. The firstpassage time between states is also given in this paper, and the theoretical computational results agree withobservational data. It is mathematically and thoroughly verified in this paper that the nonlinear 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 Niño-Southern Oscillation (ENSO) from unstable state tostable state is studied from the point of view of nonequilibrium system dynamics. The study results reveal that although the complex nonlinear ocean-atmosphere oscillator model possesses multiequilibrium states, the real climatic system possesses a a quasi-normal state and a strong ENSO cycle stable state. The first passage time between states is also given in this paper, and the theoretical computational results agree withobservational data.