A new modeling method for a nonlinear system by using equilibrium manifold (EM) and its expansion model (EME model) was presented. The property of the EME model was discussed, and the effect of mapping design to the model has been discussed. This paper also has researched the adaptivity analysis to the EME model. Then an approximate nonlinear model for an aircraft engine is applied, followed by an identification procedure for an aircraft engine. Simulations showed good precision of this model in capturing the nonlinear behavior of nonlinearities and had the simpler structure.