  Ionization, excitation, and de-excitation to the ground state is studied
theoretically for the first excited singlet state B $^1\Sigma_u^+$ of H$_2$
exposed to intense laser fields with photon energies in between about 3 eV and
13 eV. A parallel orientation of a linear polarized laser and the molecular
axis is considered. Within the dipole and the fixed-nuclei approximations the
time-dependent Schr\"odinger equation describing the electronic motion is
solved in full dimensionality and compared to simpler models. A dramatic
break-down of the single-active-electron approximation is found and explained
to be due to the inadequate description of the final continuum states.
