A method of cleaning at least one optical component of at least one irradiation device having at least one radiation source in a vacuum chamber. The source generates in particular extreme ultraviolet and/or soft X-ray radiation whose rays are guided via the optical component onto a workpiece to be treated, during which the optical component is at least partly polluted because of an inorganic substance introduced by the radiation source. A least one reaction partner that is substantially translucent or transparent to the rays is introduced via a feeder device in dependence on the prevailing reaction conditions. The reaction partner reacts chemically with the polluting deposits so as to remove them from the optical component.