A method for operating an EUV lithography apparatus (1) with at least one vacuum housing (27) for at least one reflective optical element (12) includes operating the EUV lithography apparatus in an exposure operating mode (B), in which EUV radiation (5) is radiated into the vacuum housing, wherein a reducing plasma is generated at a surface (12a) of the reflective optical element in response to an interaction of the EUV radiation with a residual gas present in the vacuum housing. After an exposure pause, in which no EUV radiation is radiated into the vacuum housing, and before renewed operation of the EUV lithography apparatus in the exposure operating mode (B), the EUV lithography apparatus is operated in a recovery operating mode, in which oxidized contaminants at the surface of the reflective optical element are reduced in order to recover a transmission of the EUV lithography apparatus before the exposure pause.