Multilayer coatings composed of TiO(2), Ta(2)O(5), HfO(2), or Al(2)O(3) as high-index materials and SiO(2) as low-index material were investigated for laser-induced damage using 1 ps, 5 µJ pulses generated by a mode-locked Yb:YAG thin-disk oscillator operating at a wavelength of 1030 nm and repetition rate of 11.5 MHz. Previously reported linear band gap dependence of damage threshold at kHz repetition rates was confirmed also for the MHz regime. Additionally, we studied the effect of electric field distribution inside of the layer stack. We did not observe any significant influence of thermal effects on the laser-induced damage threshold in this regime.