In this Paper, we investigate a nonlinear system composed of an effective two-level atom or ion interacting with two quantized cavity fields.We propose a fairly universal intensity-dependent Raman model to describe the atomic or ionic transitions involving 2k photons.Using the standard and unified method we have put forward, we obtain the analytical expressions of the model′s energy eigenvalues and eigenvectors, evolution operator,photon number operators for the two quantized modes,as well as the atomic inversion operator.