Olefinically unsaturated carbonyl compounds R.sup.1 --CHR.sup.2 --CHR.sup.3 --C(R.sup.4)O (I) and alcohols R.sup.1 --CHR.sup.2 --CHR.sup.3 --CH(R.sup.4)--OH (II) (where R.sup.1 is an olefinically unsaturated organic radical, and R.sup.2, R.sup.3 and R.sup.4 are H or C.sub.1 -C.sub.4 -alkyl) are prepared by hydrogenating the carbonyl compounds R.sup.1 --CR.sup.2 .dbd.CR.sup.3 --C(R.sup.4)O (III) in the liquid phase with hydrogen, using a catalyst system comprising, firstly, Pd and, secondly, Ru, Rh, Os, Ir or Pt, in the presence of from 5 to 40% by weight, based on (III), of a tertiary amine, under a hydrogen pressure of from 1 to 20 bar is predominantly (I) is to be obtained and from 20 to 150 bar if predominantly (II) is to be obtained.The process is of particular importance for the hydrogenation of citral (IIIa) to give citronellal (Ia) or citronellol (IIa), the preferred amine being trimethylamine.