The EI Niño/La Niña and southern oscillation is an interannual phenomenon involved in the tropical Pacific ocean-atmosphere interactions. In this paper, the aim is to create a method of asymptotically solving the nonlinear singularly perturbed problem for the ocean-atmosphere oscillator models. And according to a class of ocean-atmosphere oscillator models, employing the singular perturbation method, we study the approximate solution of corresponding problem. The obtained results from singular perturbation method can be used for analyzing the sea surface temperature anomaly and the thermocline depth anomaly in the equatorial Pacific of the atmosphere-ocean oscillator for the EI Niño/La Niña and southern oscillation model.