TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Compound: The alkylalkanolamine has the formula R1R2NCH2CH2OH (II). The nitroxide free-radical scavenger has the formula R1a-C(R2a)(R6)-N-O-C(R3)(R5)-R4 (I).R1=3-24C (iso)alkyl group;R2=H, -CH2, -CH2CH2OH or -R1;R1a, R2a, R3 and R4=1-15C alkyl (optionally substituted by a heteroatom) (preferably methyl, ethyl or propyl);R5 and R6=1-15C alkyl (optionally substituted by halogen, cyano, -CONH2, -SC6H5, -S-COCH3, -OCOCH3, -OCOC2H5, carbonyl, alkenyl (where the double bond is not conjugated with the nitroxide moiety), or -COOR') (preferably methyl, ethyl or propyl);andR'=alkyl or aryl.R5 and R6 together forming part of a ring that contains 4 or 5 carbon atoms and up to two heteratoms selected from O, N or S. Preferred Components: The alkylalkanolamine is selected from N-alkylalkanolamines, N-alkyldialkanolamines or N-dialkylalkanolamines (preferably from butyldiethanolamine (BDEA), butylaminoethanol (BAE), dibutyl-aminoethanol (DBAE), diisopropylaminoethanol (DIPAE), octylamino-ethanol (OAE) or octyldiethanolamine (ODEA)). The nitroxide is a piperidino-1-oxyl, a pyrrolidino-1-oxyl or a pyrrolin-1-oxyl (preferably 4-hydroxy-2,2,6,6-tetramethylpiperidino-1-oxy (4-hydroxy TEMPO), 4-oxo-2,2,6,6-tetramethylpiperidino-1-oxy and 2,2,6,6-tetramethylpiperidino-1-oxy (TEMPO); especially 4-hydroxy-2,2,6,6-tetramethylpiperidino-1-oxy); or the nitroxide is di-tert-butyl-nitroxide. The fatty ester component comprises a biodiesel. Preferred Composition: The composition contains at least 1 (preferably at least 5; especially at least 10) parts per million (ppm) of the nitroxide and less than 200 (preferably less than 100, especially less than 50) ppm of the nitroxide; at least 50 ppm, preferably at least 100 ppm, especially at least 200 ppm of the alkylalkanolamine, but preferably less than 10000 ppm; and at least 10 wt.%, preferably at least 25 wt.%, especially at least 40 wt.% of the unsaturated fatty esters. Preferred Method: For making a stabilized composition, the nitroxide free-radical scavenger is dissolved in the alkylalkanolamine before being blended with the fatty ester component. The nitroxide free-radical scavenger is dissolved in a hydroxylamine, or in a mixture of a hydroxylamine and the alkylalkanolamine, before being blended with the fatty ester component. EXAMPLE - No suitable example given.