Substrates suitable for mirrors used at wavelengths in the EUV wavelength range have substrates (1) including a base body (2) made of a precipitation-hardened alloy, of an intermetallic phase of an alloy system, of a particulate composite or of an alloy having a composition which, in the phase diagram of the corresponding alloy system, lies in a region which is bounded by phase stability lines. Preferably, the base body (2) is made of a precipitation-hardened copper or aluminum alloy. A highly reflective layer (6) is preferably provided on a polishing layer (3) of the substrate (1) of the EUV mirror (5).