A generalized Floquet formalism combined with Bloch's wave operator methodology is applied to the study of adiabatic versus sudden transport mechanisms in molecular responses to ultrashort and intense laser pulses. The model considers the laser pulse as a whole to be periodic, instead of the optical cycle as in standard Floquet treatments. This leads to a better understanding of the dynamics and a considerable simplification in terms of the number of generalized Floquet eigenstates needed to accurately describe the dynamics. The method is illustrated for the phenomenon of above threshold dissociation and inelastic transitions in H₂⁺ in the presence of ultrashort (a few femtoseconds) and intense (of the order of TW cm⁻²) laser fields. It is found that, while the dissociation probabilities and fragment kinetic energy spectra can be accurately described by a single generalized Floquet eigenstate within the adiabatic limit, an accurate description of inelastic transitions requires more than one generalized Floquet state, due to the role of non-adiabatic dynamics.