A Q-switched CO2 laser material processing system with acousto-optic modulators (AOM) is employed, on the one hand, inside the resonator for Q-switching the CO2 laser and, on the other hand, externally for efficient suppression of the radiation feedback between a laser and workpiece. The frequency shift of the radiation diffracted at the AOM is taken into account which exactly corresponds to the excitation frequency of the acoustic wave in the AOM crystal under the aspect of the amplification of the radiation in the active medium. Since this frequency shift significantly reduces the amplification of the radiation, it has to be avoided in the Q-switching process, which is achieved, by means of a tandem of two AOMs with identical excitation frequencies but with the acoustic waves propagating in opposite directions in the crystal. The frequency shift advantageously suppresses radiation feedback between the laser and workpiece.