We show that the powerful method of Floquet-Green's function can be applied to both non-relativistic and relativisit problems of interaction of an electron with a binding potential and a strong electromagnetic field. In part I we present the solution of the Schrödinger associated with a 1D polymer crystal subjected to a strong laser field, where the crystal potential is represented by a periodic delta potential and discuss some of the consequences. In part II, we give the exact solution of the relativistic problem of a Dirac electron interacting with a model-potentialandan e.m. field. The potential is chosen to support a bound state as well as the entire set of continum states of the electron in the absence of the field. The total Feynman propagator and the total wave function of the system, satisfying the Stükelberg-Feynman boundary condition are given in the useful Floquet representation. The basic transition amplitude for transition of the electron from the state () to (s′), where,, ands,s′ are the momentum and spins of the electron, due to absorption or emission of N-photons is obtained.