The invention relates to the use of compounds of general formula (I): CH3(-CH=CH)3-R (I) wherein R is selected from CO-O-R' or CO-O(-), R' being selected from H, alkyl or alkenyl from C1 to C22, or sugars, and their pharmaceutically acceptable salts, preferably such as sodium, potassium, or lysine salts, each compound of general formula (I) being used as such or mixed with one or more of the others, as active ingredients in a pharmaceutical or cosmetic composition provided with antioxidant activity against free radicals.