  We study the dissociation of H$_2$$^+$ in uv laser pulses by solving the
non-Born-Oppenheimer time-dependent Schr\"{o}dinger equation as a function of
the photon energy $\omega$ of the pulse. Significant enhancements of the
dissociation into highly excited electronic states are observed at critical
$\omega$. This is found to be attributed to a sequential resonant excitation
mechanism where the population is firstly transferred to the first excited
state by absorbing one photon and sequentially to higher states by absorbing
another one or more photons at the same internuclear distance. We have
substantiated the underlying dynamics by separately calculating the nuclear
kinetic energy spectra for individual dissociation pathways through different
electronic states.
