The invention relates to a composition for pharmaceutical or nutritional or cosmetic use, formulated for oral or topical use and possessing antioxidant activity against free radicals, comprising: a) a Vitis vinifera seed, or seed and leaf, extract containing a combination of the flavonoids catechin and quercetin in a molar ratio in a range from 6:1 to 3:1, respectively, or a') a Vitis vinifera seed, or seed and leaf, extract containing a combination of the flavonoids catechin and quercetin in a molar ratio in a range from 7:1 to 4:1, respectively, or a") a mixture of Vitis vinifera extracts a) and a'), or a'") a mixture of catechin and quercetin in a molar ratio in a range from 7:1 to 3:1, respectively, together with b) an olive, Olea europaea L, leaf extract having a hydroxytyrosol content in a range from 1 % to 30% by weight of the extract, or b') hydroxytyrosol in an amount equal to that contained in the b) extract.