We reconsider the Born-Oppenheimer-Huang treatment of systems of electrons and nuclei for the case of their interaction with time-dependent fields. Initially, we present a framework in which all expressions derived are formally exact since no truncations are introduced. The objective is to explore the general structure of the equations under the most unrestricted conditions, including the possibility that the electronic basis is dependent both on the nuclear coordinates and on time. We then derive an application of the theory applicable to cases of interaction with strong time-dependent fields. The method truncates the electronic basis only after the time-dependent interaction is taken into account in the electronic wave functions. This leads to theory which is similar to a Born-Oppenheimer-type truncation within the interaction picture. (C) 2003 American Institute of Physics.