An optical assembly is mounted in a projection exposure apparatus (101) for EUV microlithography and includes at least one vacuum chamber (70, 71, 68a), at least one optical element (6, 7; 65, 66; 63) arranged in the vacuum chamber (70, 71, 68a), the optical element (6, 7; 65, 66; 63) having an optical surface (18) arranged to be impinged upon by a useful beam bundle (3) of the projection exposure apparatus (101), and a cleaning device (72) configured to clean the optical surface (18). The cleaning device (72) is configured to perform particle cleaning of the optical surface (18) at a gas pressure within the vacuum chamber (70,71, 68a) which is higher than a vacuum pressure (po) for performing an exposure operation with the projection exposure apparatus (101). As a result, optical elements having respective optical surfaces arranged to be impinged upon by a useful beam bundle can be cleaned reliably of foreign particles.