A multilayer system and its production. Multilayer systems, such as those used as mirrors in the extreme ultraviolet wavelength range, suffer contamination or oxidation during storage in air and in long-time operation, i.e. when exposed to EUV radiation in a vacuum environment with certain partial pressures of water or oxygen, which causes a serious reduction in reflectivity. The multilayer system according to the invention will have a long life with constantly high reflectivity. Their reflectivity can be enhanced by barrier layers. The multilayer systems according to the invention have protective layers comprising iridium. The multilayer systems according to the invention are produced by direct, ion-beam-supported growth of the respective layer. The multilayer systems according to the invention are not only resistant to contamination and oxidation, but can also be cleaned if necessary, without losing reflectivity. Because of their long life with constantly high reflectivity, they are particularly suitable for use in semiconductor lithography in the soft X-ray range or extreme ultraviolet wavelength range.