TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Component: The Group VIII metal of the homogenous catalyst is rhodium, ruthenium, palladium, cobalt, platinum, nickel, iridium, and/or iron.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Component: The unsaturated fatty acid alkyl esters used as the starting material for the hydrogenation follow formula R1CO-OR2 (I). The hydrophilic ligand of homogenous catalyst is hydrophilic phosphines, amines, and oxygen containing ligands. The homogeneous catalyst is a complex of rhodium or ruthenium or palladium and trisulfonated triphenylphosphine. The co-catalyst is tetraalkylammonium salt or an esterquat or lecithin that is inherent in the crude unsaturated fatty acid esters and glyceride renewable starting material mixture. The cationic surfactant is octyltrimethylammonium chloride, dodecyltrimethylammonium chloride, tetradecyltrimethylammonium chloride, cetyltrimethylammonium chloride, cetylpyridinium chloride, octadecyltrimethylammonium chloride, distearyldimethylammonium chloride, dicocoylmethylethoxymonium methosulfate, or distearoylmethylethoxymonium methosulfate. The solvent is diethyl ether, pentane, hexane, and/or toluene.R1CO=acyl radical having 6-22C and 0-3 double bonds; andR2=alkyl having 1-4C.Preferred Composition: The unsaturated fatty acid alkyl esters comprise at least 60 mol.% 18C residues. The molar ratio between the Group VIII metal and the hydrophilic ligand is 1:1-1:6. The content of the Group VIII metal in the reaction mixture is 10-50 ppm. The molar ratio of C=C/Group VIII metal is 500-25000. The molar ratio between co-catalyst and ligand is 1:2-1:20. The ratio between the volume of the aqueous and the organic phase is 7:1-1:5. Preferred Process: Methyl or ethyl esters of linseed, soybean, or sunflower fatty acid are subjected to hydrogenation. The hydrogenation takes place in the presence of a co-catalyst from cationic, zwitterionic, nonionic and anionic surfactants, ionic liquids, or phase transfer catalysts. The hydrogenation takes place in an aqueous/organic two-phase system, formed by the aqueous catalyst solution and the polyunsaturated fatty acid alkyl ester or glyceride. The pH value of the aqueous phase is adjusted to 7. The organic solvent is added to the organic phase. The hydrogenation is conducted at 50-120 degrees C and under pressure of 5-100 bar for 5-240 minutes. Once the hydrogenation has been finished the phases are separated, the organic phase comprising the hydrogenation product is purified and the aqueous phase comprising the catalyst is recycled. EXAMPLE - A flask was charged with 279 g linseed oil and a solution of 182.8 g methanol containing 2.79 g sodium hydroxide. The mixture was stirred at 55 degrees C for 100 minutes. The course of the reaction was followed by thin layer chromatography. The reaction mixture was cooled and stirred for 8 hours at room temperature. After phase separation resulted in the isolation of the methyl esters of linseed oil (MELO) and the glycerol. The glycerol phase (bottom layer) was removed and kept in a separate container. The MELO phase (top layer) was washed with distilled water (pH 7.0), dried over sodium sulfate to obtain 210 g MELO mixture used as starting material in the hydrogenation reaction without any purification by distillation. Methyl esters composition of linseed oil was determined by gas chromatography. The result showed 65.8 mol.% methyl alpha -linolenate.