In most places where molecular hydrogen exists in the interstellar medium, it will be found in the ground vibrational and ground electronic state. This will not be so, however, near 0 or early B stars where, in the region just beyond the ionization boundary, populations will be determined by UV fields up to 105 times more intense than the mean interstellar value (4 × 10−16 ergs cm−3 s−1 = 1 Habing unit). The H2 absorbs Lyman-Werner band photons longwards of λ91 nm and subsequent decays to the ground electronic state may lead to dissociation (vibrational continuum) or to one of 14 vibrationally excited states. Molecules in these states have lifetimes of order 1010 s and, in the intense fields, will be exposed to further Lyman-Werner excitation. The probability of dissociation is therefore greatly enhanced by this ‘multiple excitation’, since the number of lines available to vibrationally excited H2 is many times that available to ground-state H2 (Shull, 1978).