For a working wavelength in the range from 1 nm to 12 nm, a reflective optical element has, on a substrate, a multilayer system that includes at least two alternating materials having a different real part of the refractive index at the working wavelength. The multilayer system includes a first alternating material from the group formed from thorium, uranium, barium, nitrides thereof, carbides thereof, borides thereof, lanthanum carbide, lanthanum nitride, lanthanum boride, and a second alternating material from the group formed from carbon, boron, boron carbide, or lanthanum as first alternating material and carbon or boron as second alternating material. It has, on the side of the multilayer system remote from the substrate, a protective layer system including a nitride, an oxide and/or a platinum metal.