For the production of mirrors for EUV lithography, substrates are suggested having a mean relative thermal longitudinal expansion of no more than 10 ppb across a temperature difference ΔT of 15° C. and a zero-crossing temperature in the range between 20° C. and 40° C. For this purpose, at least one first and one second material having low thermal expansion coefficients and opposite gradients of the relative thermal expansion as a function of temperature are selected and a substrate is produced by mixing and bonding these materials.