A theoretical framework for the description of the pulse-induced reaction dynamics of molecules interacting with short, intense laser pulses is derived. Born-Oppenheimer adiabaticity is formulated in terms of quasistationary Floquet states; its violation and the structure of the potential mixing electronic levels, and thus effecting this violation, is discussed; it is shown that, on the basis of quasistationary states, this potential is (to a very good approximation) nonvanishing only around near degeneracies in the quasienergy spectrum where it has a simple two-level structure. Ab initio calculations showing the effectivity of this scheme are performed for the H-2 molecule. Particular emphasis is put on bond-softening reactions; a new mechanism is described.