A process for the selective hydrogenation of aromatic groups of organic molecules carrying at least one aromatic group and one epoxy group with hydrogen in the presence of a ruthenium-containing catalyst, in which a homogeneous ruthenium catalyst is used which can be prepared by reducing the ruthenium compound with a metal having a redox potential of from -0.75 to 2.5 V, a boron hydride, an aluminum hydride, an aluminum alkyl compound, a lithium alkyl compound, or a lithium aryl compound in the presence of an ether.