A cleaning arrangement for an optical system and in particular for an optical system designed for EUV radiation. The cleaning arrangement has a gas inlet (28) for a reactive gas (29). Contaminants (23) that have deposited on the surface of optical elements (110) are detached by the reactive gas. Also provided are getter surfaces (32) that are preferably arranged opposite the surfaces to be clean and by which the contaminants detached from these surfaces are absorbed. This absorption may take place as a result of condensation on the getter surface and also by chemical reaction.