The invention relates to processes for connecting an optical element of a microlithographic projection exposure apparatus to a mount, and also relates to an assembly. A process includes the following steps: forming a substance mixture at a processing temperature from at least a first component, which is solid at the processing temperature, and a second component, which is liquid at the processing temperature, the first component being dispersed in the second component, introducing the substance mixture in the unset state between the optical element and the mount, and setting the substance mixture so as to form a diffusion alloy from the first and second components.