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.