The laser-induced damage of mixtures of Sc2O3, HfO2, Al2O3 with SiO2 has been characterized in the infrared for both nanosecond and subpicosecond pulses. Laser-induced damage thresholds (LIDTs) are reported and discussed versus band gap for different compositions. The distributions versus fluence of nanosecond damage precursor densities are extracted fitting damage probability curves. Two models are used: first, a statistical approach, i.e., direct calculation of damage precursor density from damage probability, and second a thermal model based on absorption of initiator. The results show a good agreement. The nature, shape, and size of these precursors are discussed. The critical temperature in the thermal model is dependent on the band gap energy.