Reflective optical element for an operating wavelength of between 150 nm and 300 nm in the DUV or VUV wavelength range, comprising a substrate, a dielectric layer system and a metallic coating between the substrate and the dielectric layer system, wherein the dielectric layer system comprises at least respectively one layer composed of a material having a lower refractive index n1 at the operating wavelength, and also one layer composed of a material having a higher refractive index n2 at the operating wavelength, characterized in that the dielectric layer system furthermore comprises layers composed of a material having a refractive index n3 at the operating wavelength, where n1<n3<n2, wherein a layer having a medium refractive index n3 is arranged at transitions from a layer having a lower refractive index n1 to a layer having a higher refractive index n2 and/or from a layer having a higher refractive index n2 to a layer having a lower refractive index n1, in such a way that the dielectric layer system comprises a four-layer sequence of (LMHM)m or (HMLM)m where L is the layer composed of a material having a lower refractive index n1 at the operating wavelength, H is the layer composed of a material having a higher refractive index n2 at the operating wavelength and M is in each case the layer composed of a material having a refractive index n3 at the operating wavelength, wherein n1<n3<n2, and m is the number of four-layer sequences in the dielectric layer system, wherein for an operating wavelength in the range of between 240 nm and 300 nm, the at least one layer composed of a material having a lower refractive index n1 is composed of one or more materials of the group aluminium fluoride, cryolite, chiolite, lithium fluoride and magnesium fluoride, the at least one layer composed of a material having a higher refractive index n2 is composed of one or more materials of the group yttrium oxide, hafnium oxide, scandium oxide, zirconium oxide, aluminium nitride and synthetic diamond, and the layers composed of a material having a medium refractive index n3 are composed of one or more materials of the group barium fluoride, gadolinium fluoride, lanthanum fluoride, neodymium fluoride, dysprosium fluoride, aluminium oxide, yttrium fluoride, ytterbium fluoride and silicon dioxide, and wherein for an operating wavelength in the range of 150 nm to 240 nm, the at least one layer composed of a material having a lower refractive index n1 is composed of one or more materials of the group aluminium fluoride, cryolite, chiolite, lithium fluoride and magnesium fluoride, the at least one layer composed of a material having a higher refractive index n2 is composed of one or more materials of the group neodymium fluoride, gadolinium fluoride, dysprosium fluoride, lanthanum fluoride and aluminium oxide, and the layers composed of a material having the medium refractive index n3 are composed of one or more materials of the group magnesium fluoride, yttrium fluoride and silicon dioxide. wherein for an operating wavelength in the range of between 240 nm and 300 nm, the at least one layer composed of a material having a lower refractive index n1 is composed of one or more materials of the group aluminium fluoride, cryolite, chiolite, lithium fluoride and magnesium fluoride, the at least one layer composed of a material having a higher refractive index n2 is composed of one or more materials of the group yttrium oxide, hafnium oxide, scandium oxide, zirconium oxide, aluminium nitride and synthetic diamond, and the layers composed of a material having a medium refractive index n3 are composed of one or more materials of the group barium fluoride, gadolinium fluoride, lanthanum fluoride, neodymium fluoride, dysprosium fluoride, aluminium oxide, yttrium fluoride, ytterbium fluoride and silicon dioxide, and wherein for an operating wavelength in the range of 150 nm to 240 nm, the at least one layer composed of a material having a lower refractive index n1 is composed of one or more materials of the group aluminium fluoride, cryolite, chiolite, lithium fluoride and magnesium fluoride, the at least one layer composed of a material having a higher refractive index n2 is composed of one or more materials of the group neodymium fluoride, gadolinium fluoride, dysprosium fluoride, lanthanum fluoride and aluminium oxide, and the layers composed of a material having the medium refractive index n3 are composed of one or more materials of the group magnesium fluoride, yttrium fluoride and silicon dioxide.