A class of coupled system of the El Nino/La Nina-Southern Oscillation (ENSO) mechanism is studied. Using the perturbed theory, the asymptotic expansions of the solution for ENSO model are obtained and the asymptotic behavior of solution for corresponding problem is considered. Using the perturbed theory, the asymptotic expansions of the solution for ENSO model are obtained and the asymptotic behavior of solution for the corresponding problem is considered.