Dimer fatty acids are produced from different fatty acids by heating. Necessary are a fatty acid with conjugated double bonds or other unsaturated fatty acids. Examples of such fatty acids are conjugated linoleic acids. The reaction is carried out via Diels-Alder addition, whereby a partially unsaturated C6 ring is formed. Besides the dimer, trimers as well as (unreacted) monomers of the fatty acids may be present in the mixture.