Femtosecond pump/probe multiphoton ionization experiments on Na2 molecules are performed. The dependence of the total Na2+ ion signal on the delay time and the intensity of the femtosecond laser pulses is studied in detail. It is observed that molecular vibrational wavepacket motion in different electronic states dominates the time dependence of the ion signal. For higher laser intensities the relative contributions from the A 1SIGMA(u)+ and the 2 1PI(g) states change dramatically, indicating the increasing importance of a two-electron versus a one-electron process. For even stronger fields (10(12) W/cm2) a vibrational wavepacket in the electronic ground state X 1SIGMA(g)+ is formed and its dynamics is also observed in the transient Na2+ signal. Time-dependent quantum calculations are presented. The theoretical results agree well with the experiment.