The problem of multiphoton processes for intense, long wavelength irradiation of atomic and molecular electrons is presented. The recently developed method of quasi-adiabatic time evolution is used to obtain a non-perturbative analysis. When applied to the standard vector potential coupling, exact auxiliary equations are obtained, which correspond to the electric dipole coupling. A time-dependent solution is then achieved through application of the Goepper-Mayer gauge. In the talk, we will discuss the study of the Rydberg atom. Numerical investigations of the auxiliary equations show evidence of multiphoton transitions and allow us to obtain the quantum Floquet states and quasienergies of the system.