In a process for hydrogenating at least one organic compound, the organic compound or compounds is/are brought into contact with a hydrogen-containing gas in the presence of a catalyst which comprises, as active metal, ruthenium either alone or together with at least one further metal of transition group I, VII or VIII of the Periodic Table applied to a support material based on amorphons silicon dioxide and is obtainable by: i) a single or multiple treatment of a support material based on amorphous silicon dioxide with a halogen-free aqueous solution of a low molecular weight ruthenium compound and subsequent drying of the treated support material at below 200.degree. C., ii) reduction of the solid obtained in i) by means of hydrogen at from 100 to 350.degree. C., with step ii) being carried out directly after step i).