Method for producing fatty alcohols includes splitting vegetable oils and animal fats under pressure into fatty acids and glycerol in counterflow to steam. The reaction product is physically separated into fatty acids and sweet water containing glycerol. The fatty acids are subjected to a distillation, and the separated fatty acid fraction is mixed together with fatty alcohol at 230 to 270° C. and atmospheric pressure. The wax esters obtained by esterification are hydrogenated to fatty alcohols by adding hydrogen on a fixed-bed catalyst, and the reaction product is separated into fatty alcohols and hydrogen. The wax esters are hydrogenated on a fixed bed of uniformly shaped catalyst bodies produced by extrusion, which consist of the main components copper and copper-chromium oxide and the secondary components zinc, aluminum, iron, silicon and alkaline earth elements, at 180 to 220° C. and 70 to 100 bar(a).