Laser damage thresholds of ZrO2, TiO2 and HfO2 films of optical thickness lambda, (lambda = 248 nm) evaporated on quartz glass substrates were investigated with the photoacoustic probe beam deflection technique in a 1-on-1 irradiation mode for a range of fluences from below to above the thin-film laser damage threshold. In addition, irradiated spots were investigated systematically by a video imaging difference technique. It is demonstrated that the photoacoustic technique allows a more sensitive and precise determination than optical inspection of the onset of damage. An exponential dependence of damage thresholds on the apparent band gap of the respective thin-film material, as determined by optical absorption spectroscopy, was found. Results for amorphous and polycrystalline films on BK7 glass and SQ1 quartz substrates are compared and the influence of a SiO2 protective coating on the laser-damage threshold is investigated.