A method of producing extreme ultraviolet radiation (EUV) or soft X-ray radiation by means of an electrically operated discharge, in particular for EUV lithography or for metrology, in which a plasma (22) is ignited in a gaseous medium between at least two electrodes (14, 16) in a discharge space (12), said plasma emitting said radiation that is to be produced. The gaseous medium is produced from a metal melt (24), which is applied to a surface in said discharge space (12) and at least partially evaporated by an energy beam, in particular by a laser beam (20).