Suggested is a process for the manufacture of unsaturated fatty acid alkyl esters or glycerides having a total content of C 18:1 of about 30 to about 80 Mol-% by partial hydrogenation of unsaturated fatty acid esters having a total content of (C18:2+C18:3) of at least 65 Mol-%--calculated on the total amount of C18 moieties in the ester--which is characterised in that the hydrogenation is conducted in an aqueous/organic two phase system in the presence of a water soluble catalyst consisting of a Group VIII metal and a hydrophilic ligand.