The invention relates to an illumination system for an EUV lithography device, comprising: a first facet mirror having facet elements that reflect EUV radiation, and a second facet mirror having facet elements for reflecting the EUV radiation reflected by the first facet mirror onto an illumination field. At least one of the facet elements of the first facet mirror or of the second facet mirror is designed as a diffractive optical element for diffracting the EUV radiation. In particular, at least one of the facet elements of the second facet mirror is designed as a diffractive optical element for illuminating only a part of the illumination field. The invention also relates to an EUV lithography device comprising such an illumination system, and to a facet mirror comprising at least one diffractive facet element.