  It is shown that, under sufficiently intense OB-star illumination of a
stationary photoexcitation front (PDR), nonlinear H2 photoexcitation processes
comprising driven resonant two-photon transitions between X-state quantum
levels, with VUV continuum light from the star supplying both driving fields,
largely determine the photonic pathways of H2 molecules in the PDR close to the
ionization front. Specifically, for a PDR irradiated by a 0.1-pc-distant B0 III
star, the total rate at which an H2 molecule is nonlinearly photoexcited out of
any X-state quantum level is calculated to be roughly 100 times greater than
the total rate at which it is linearly photoexcited out of the same level. In
strongly excited PDRs, the populations in almost all of the ~300 bound quantum
levels of the X state will be maintained approximately equal via a few myriads
of interconnecting two-photon steps. The remarkable importance of two-photon
transitions in H2 photoexcitation in strongly irradiated PDRs derives from the
exceptionally narrow Raman linewidth that characterizes all two-photon
transitions between bound H2 X-state quantum levels.
