Ionization and dissociative ionization of N2, CO, CS2, CO2 and NO2 by intense 532 nm radiation has been studied by measuring mass spectra at incident laser intensities over the range 4.1*1012-1.27*1014 W cm-2, covering a region which is intermediate between the multiphoton and tunnelling regimes. For molecules with large zero-field dissociation energies (N2, CO) the mass spectra show the dominance of the molecular ion peak, with relatively small yields of fragment ions. For molecular species which are more loosely bound (CS2, CO2 and NO2), fragment ions dominate the mass spectra. The results appear to indicate that, at 532 nm, molecules with a low zero-field dissociation energy (less than approximately 6 eV) tend to dissociate first, followed by ionization of the fragments. In the case of molecules with high zero-field dissociation energies, molecular ionization occurs first, followed subsequently by fragmentation.