Acid-resistant copper oxide-chromium oxide catalysts for hydrogenation of fatty acids or fatty acid mixtures and/or the esters thereof are obtained through heat treatment of copper oxide and chromium oxide or of precursor compounds that are convertible into copper oxide or chromium oxide and which contain aluminum zirconium, cerium and/or lanthanum oxide as an additional metal component. The acid resistance is defined by the fact that the amount of copper which is dissolved by stirring 10 g of the catalyst for 2 minutes in 100 ml of 10 weight percent acetic acid at 20.degree. C., is a maximum of 200 mg.