We take into account the two-photon process and generalize the Jaynes-Cummings (JC) model to the case of atomic level degenerate in the projections of the angular momenta, and we establish two-photon degenerate JC models with and without the rotating-wave approximation (RWA) quantum theory. Comparing the atom population inversion of the generalized JC model with that of the original JC model, we found that the revival period of the degenerate JC model becomes longer and the maximum amplitude of atomic inversion decreases with RWA. Without RWA, the quantum chaos of the generalized JC model is much weaker than that of the original JC model