Abstract: The ENSO(El Ni o/La Ni o Southern Oscillation) is an exceptional event in the tropical atmosphere and ocean. It describes phenomenon of circular climate. ESNO event is a larger scale ocean-atmosphere coupled system, which affects global climate. It is a complicated nonlinear system. Its appearance affects badly climate for the global each area and the environment and so on. The global economic development and human living are gotten grievous influence and it brings many calamities. Thus to study its rule and prevention there is recently very attractive object of study in the international academic circles. Many scholars made more studies for its local and whole behaviors using different methods, such as self-anamnestic principle, by the method of Fokker-Plank equation, and the higher order singular pedigree and predictable study, rapid change on boundary, indeterminate adapive cortrol, multi-cogradient method, perturbed situation and so on. Nonlinear perturbed theory is a very attractive object of study in the international academic circles. Many scholars considered a class of singularly perturbed nonlinear boundary value problems for the ordinary differential equation, the reaction diffusion equations, the boundary value problems of elliptic equation, the initial boundary value problems of hyperbolic eqaution, the shock layer solution of nonlinear equation for singularly perturbed problem and so on. In this paper, the sea-air phenomena ENSO in a class of atmospheric physics is discussed. Under suitable conditions, using a perturbed theory and method, we obtain simple and rapid arbitrary order to approximate asymptotic expansion of solution for the corresponding nonlinear problem.