A process for preparing saturated branched chain fatty acids or alkyl esters thereof involving subjecting unsaturated fatty acids having 10 to 25 carbon atoms, alkyl esters thereof or mixtures thereof to a skeletal isomerization reaction in the presence of water or a lower alcohol at a temperature of about 240° C. to about 280° C. using a combination of a stericly hindered Lewis base and zeolite as a Brönsted or Lewis acid catalyst, and isolating saturated branched chain fatty acids or alkyl esters thereof or mixtures thereof from the reaction mixture obtained by the skeletal isomerization reaction. The yield of said saturated branched chain fatty acids is ≧70 wt %. The stericly hindered Lewis base is a tertiary amine or phosphine with linear or branched C1 to C6 alkyl or phenyl groups attached thereto.