Abstract: For the oligomerization of a fatty ester or fatty acid containing conjugated double bonds, the reaction uses a catalyst consisting of an activated earth, e.g., montmorillonite, at a temperature of from 100.degree.-180.degree. C., preferably from 130.degree.-160.degree. C. The process can be carried out continuously or in a batch process on a fixed bed and is particularly applicable to conjugated methyl esters obtained by conjugating and transesterifying sunflower seed oil. The oligomerized products obtained are particularly useful as lubricants or polycondensation reactants.