A reflective optical element e.g. for use in EUV lithography, configured for an operating wavelength in the soft X-ray or extreme ultraviolet wavelength range, includes a multilayer system (20) with respective layers of at least two alternating materials (21, 22) having differing real parts of the refractive index at the operating wavelength. Preferably, at least at an interface from the material (21) having the higher real part of the refractive index to the material (22) having the lower real part of the refractive index, a further layer (23) of a nitride or a carbide of the material (22) having the lower real part is arranged. Particularly preferably the material (22) having the lower real part of the refractive index is lanthanum or thorium. Preferably, the layers (21, 22, 23) of at least one material are applied in a plasma-based process for manufacturing a reflective optical element as described.