We study the breakup of H + 2 exposed to super-intense, femtosecond laser pulses with frequencies greater than that corresponding to the ionization potential. By solving the time-dependent Schrödinger equation in an extensive field parameter range, it is revealed that highly nonresonant dissociation channels can dominate over ionization. By considering field-dressed Born-Oppenheimer potential energy curves in the reference frame following a free electron in the field, we propose a simple physical model that characterizes this dissociation mechanism. The model is used to predict control of vibrational excitation, magnitude of the dissociation yields, and nuclear kinetic energy release spectra. Finally, the joint energy spectrum for the ionization process illustrates the energy sharing between the electron and the nuclei and the correlation between ionization and dissociation processes. [8,9], and rescattering induced dissociation [10]. All these processes were discovered in the low-frequency regime where absorption of several photons is needed to reach a breakup channel. Depending on the laser parameters, either dissociation or ionization dominates [11][12][13].With advancements in light-source technology, extreme-ultraviolet (XUV) laser pulses of femto-and subfemtosecond duration are now produced from highorder harmonic [14][15][16][17] or free-electron lasers [18,19]. New focusing techniques [20][21][22] led to XUV femtosecond (fs) pulses with peak intensities I ≥ 4 × 10 17 W/cm 2 [23]. Intense XUV pulses were, e.g., applied on rare gases to study sequential versus non-sequential multiple ionization [24,25], and creation of charge states up to 21 in Xe was observed [21]. For molecules, experiments on HeH + [26] and N 2 [27] provided benchmark data for theory. The high-frequency regime is defined in this work as the regime where one-photon ionization is allowed. Since the photon resonance is much closer to the threshold for ionization than for dissociation, ionization is at first glance expected to dominate.Here we characterize some hitherto unobserved molecular breakup phenomena in the regime of super-intense, high-frequency, fs pulses, supplementing the phenomena known from the low-frequency regime, and adding insight to the general field of strong laser-matter interaction. The characteristics we find include (a) even with full inclusion of nuclear dynamics, stabilization against ionization occurs, i.e., the ionization yield does not necessarily increase with intensity [28,29]; (b) a mechanism by which dissociation, in contrast to the expectation from energy considerations, completely dominates over ionization; (c) control over the vibrational distribution, dissociation yield, and nuclear kinetic energy release (NKER) spectra by the parameters of the laser pulse; (d) insight into the energy sharing between electronic and nuclear degrees of freedom, as displayed by the joint energy spectrum (JES).We consider H + 2 , a molecule that was used to discover many low-frequency processes that were later observed in m...