Abstract: A mirror system comprises: an EUV mirror having an optical surface having a high reflectivity for EUV radiation; and a frame structure carrying a system component of the mirror system. The frame structure comprises a structure body and an insert. The insert comprises (or consists of) a material whose thermal properties deviate from the thermal properties of the material of the structure body. A fluid channel for a temperature-regulating fluid is formed in the structure body. The insert is exposed to a heat load during operation of the mirror system. The insert spans a contour line transversely to the direction of the fluid channel so that a cross-sectional portion of the fluid channel is accommodated within the contour line. The disclosure furthermore relates to a microlithographic projection exposure apparatus comprising such a mirror system.