Mixtures of cedar polyphenols and thiodipropionic acid exhibit synergistic antioxidant effects when added to animal fats and vegetable oils and foodstuffs containing these materials. The amount of the polyphenol component of the mixture should be at least equal to the amount of thiodipropionic acid therein. These cedar polyphenol-thiodipropionic acid additives greatly increase the storage life of fats and oils when added thereto in amounts of at least about 50 per million.