The dynamics of molecular electron excitation and ionization is studied in real time for ultra-short IR laser pulses of intensity I > 10(13) W/cm(2). The multi-electron molecule is modeled by a system of two active electrons moving in the field of the frozen core. The time dependence of electron probability, electron energy, and one-electron/two-electron ionization probability are calculated for the example of the N-2 molecule and a laser pulse with lambda = 800 nm, tau = 5 fs. The electron dynamics of the pulse-excited molecule is considered also after the pulse end. The results show that in strong IR pulses of I greater than or equal to 10(16) W/cm(2) the molecule undergoes a cascade ionization, where the one electron is emitted with the same probability as a pair of electrons.