Exact numerical solutions of the time dependent Schroedinger equation, TDSE, of one and two electron molecules and ions allow us to investigate the highly nonlinear, nonperturbative behavior of such systems in the presence of ultrashort(t<50 femtoseconds),intense(I⩾1014&hthinsp;W/cm2)laser pulses. Quasistatic models of ionization lead to a qualitative understanding of a universal phenomenon occurring in these extreme conditions: Charge Resonance Enhanced Ionization, CREI. Exact non-Born Oppenheimer TDSE simulations of the dissociative-ionization ofH2+lead to the conclusion that CREI is responsible for anomalous kinetic energy distributions observed in Coulomb Explosion experiments, i.e., Coulomb explosions are non-Franck-Condon and occur at critical internuclear distancesRcand geometries. Analytic formulas are obtained forRcwhich are shown to arise from charge resonance or transfer induced at the maximum field strength of the laser fields. ©2000 American Institute of Physics.