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The paper presents the results of surface radiation erosion and stress evolution of multilayer coatings made of ZrN ceramic layers and metallic glass (Zr-Cu) under He2+ ion irradiation with an energy of 40 keV and fluences from 5·1016 to 1.1·1018 cm−2. Multilayer coatings of nc-ZrN/a-Zr1−хCuх with an elementary layer thickness of 5 nm/5 nm and 5 nm/10 nm are formed by reactive magnetron sputtering with different copper Cu contents (x = 0.45; 0.53; 0.61 and 0.74). Sputtering took place from Zr and Cu targets at a substrate temperature T = 300 °C. The surface of the films remained stable up to a fluence of 5·1017 cm−2. It has been found that with an increase in the ion fluence, the radiation erosion of the surface develops according to the flecking mechanism. It has been established that an increase in the thickness of the amorphous layer and the copper content increase the resistance to irradiation (the critical fluence increases from 5·1017 cm−2 to 8·1017 cm−2). Irradiation with helium He ions leads to a decrease in the level of compressive stresses. Reducing the level of stresses in multilayer films is associated with the effects of changes in the microstructure of the layers (shape distortion) at a dose of 2·1017 cm−2 and radiation erosion at a dose of 8·1017 cm−2.