A method of generating in particular EUV radiation (12) and/or soft X-ray radiation (12a) emitted by a plasma (26) is described. The plasma (26) is formed by an operating gas (22) in a discharge space (14) which comprises at least one radiation emission window (16) and an electrode system with at least one anode (18) and at least one cathode (20). This electrode system transmits electrical energy to the plasma (26) by means of charge carriers (24) introduced into the discharge space (14). It is suggested for obtaining a reliable ignition of the plasma (26) at high repetition frequencies that a radiation (30) generated by at least one radiation source (28) is introduced into the discharge space (14) for making available the discharge carriers (24).