Compositions containing unsaturated fatty esters may be stabilized against atmospheric oxidation by the addition of an antioxidant package containing a phenolic oxidant and a nonphenolic oxygen scavenger, which may be a hydroxylamine, an amine N-oxide, an oxime, or a nitrone. If an amine N-oxide is used, it may be used with or without a phenolic antioxidant. Compositions treated in this manner show good resistance to atmospheric oxidation and resultant viscosity increase.