Fatty acids and esters which contain only one double bond have interesting properties such as high oxidation stability or favourable pour points. For these reasons such products find a broad field of application for instance in the sections cosmetics, textile finishing agents or oilfield chemicals. However, natural fats and oils contain often multi-unsaturated fatty acids such as linoleic and linoleinic acid which are able - even in minor amounts - to change substantially the physical and chemical properties of the fatty material. Therefore, a hydrogenation procedure is needed which enables the selective conversion of multi-unsaturated into mono-unsaturated fatty acids without formation of completely saturated compounds. After a review of the general possibilities in selective hydrogenation a new method is described to hydrogenate with solvent-stabilized palladium colloid catalysts. A remarkable high selectivity was obtained applying very mild reaction conditions. By use of the liquid-liquid two phase technique an easy and complete catalyst recycle is possible.