A few years ago, we developed an approach to treat molecular systems exposed to an external, intense, time-dependent field (J. Phys. Chem. A 2003, 107, 4724; J. Chem. Phys. 2003, 119, 6998). Within this study, we encountered two novel concepts: the dressed (namely, field affected) time-dependent nonadiabatic coupling term and the space-time contours. In the present article, we analyze the newly introduced nonadiabatic coupling term and discuss its importance for dynamical studies. We also refer to the just mentioned space-time contour and present the more efficient contour for realistic situations. The scope of the above-mentioned articles is extended with the aim of defining quasi-adiabatic states for such situations. Strictly speaking, molecular systems exposed to intense, fast oscillating fields are not expected to form adiabatic states. Still we consider such a situation and end up with three possibilities for quasi-adiabatical time-dependent states eventually to be used within the Born-Oppenheimer approximation.