Mono-unsaturated fatty acids or their derivates are produced by hydrogenating poly-unaturated fatty acids or their derivates at 0° to 150° C., in a pressure range from 800 to 1500 hPa, with hydrogen and in the presence of a catalyst system that contains: a) a palladium salt and b) a carbonic acid ester, as well as, if necessary, c) a base for neutralizing the acids formed during the reduction of the palladium salt, d) water and/or a water-immiscible, inert solvent.
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