We investigate some new features of different nonlinear time-dependent models. We consider the time-dependent interaction between an atom (or more) and cavity field for one-mode and two-mode cavity fields. The idea of using the explicit time-dependence on the atom-field couplings, but for extended models are presented. The models describe one- and two-photon process and include detuning parameters, nonlinear Kerr-medium, Stark-shift and intensity-dependent coupling. Numerical investigations are used to test the quantum entanglement, geometric phase, atomic population inversion, phase...