Cosmetic composition comprising, in a cosmetically acceptable medium, at least: a) a lipophilic salicylic acid derivative of general formula below or a salt thereof derived from a mineral or organic base: in which: - the R radical denotes a linear, branched or cyclic, saturated aliphatic chain containing from 2 to 22 carbon atoms; an unsaturated chain containing from 2 to 22 carbon atoms and comprising one or more double bonds that may be conjugated; an aromatic ring bonded to the carbonyl radical directly or via saturated or unsaturated aliphatic chains containing from 2 to 7 carbon atoms; it being possible for said groups to be substituted with one or more substituents, which may be identical or different, chosen from (a) halogen atoms, (b) a trifluoromethyl group, (c) hydroxyl groups in free form or esterified with an acid containing from 1 to 6 carbon atoms, or (d) a carboxyl function in free form or esterified with a lower alcohol containing from 1 to 6 carbon atoms; - R' is a hydroxyl group or an ester group of formula: in which R 1 denotes a linear or branched, saturated or unsaturated aliphatic chain containing from 1 to 18 carbon atoms; b) at least one antiperspirant aluminium salt or complex; and c) at least one sequestrant chosen from amino acid-N,N-diacetic acid salts. a) a lipophilic salicylic acid derivative of general formula below or a salt thereof derived from a mineral or organic base: in which: - the R radical denotes a linear, branched or cyclic, saturated aliphatic chain containing from 2 to 22 carbon atoms; an unsaturated chain containing from 2 to 22 carbon atoms and comprising one or more double bonds that may be conjugated; an aromatic ring bonded to the carbonyl radical directly or via saturated or unsaturated aliphatic chains containing from 2 to 7 carbon atoms; it being possible for said groups to be substituted with one or more substituents, which may be identical or different, chosen from (a) halogen atoms, (b) a trifluoromethyl group, (c) hydroxyl groups in free form or esterified with an acid containing from 1 to 6 carbon atoms, or (d) a carboxyl function in free form or esterified with a lower alcohol containing from 1 to 6 carbon atoms; - R' is a hydroxyl group or an ester group of formula: in which R 1 denotes a linear or branched, saturated or unsaturated aliphatic chain containing from 1 to 18 carbon atoms; - the R radical denotes a linear, branched or cyclic, saturated aliphatic chain containing from 2 to 22 carbon atoms; an unsaturated chain containing from 2 to 22 carbon atoms and comprising one or more double bonds that may be conjugated; an aromatic ring bonded to the carbonyl radical directly or via saturated or unsaturated aliphatic chains containing from 2 to 7 carbon atoms; it being possible for said groups to be substituted with one or more substituents, which may be identical or different, chosen from (a) halogen atoms, (b) a trifluoromethyl group, (c) hydroxyl groups in free form or esterified with an acid containing from 1 to 6 carbon atoms, or (d) a carboxyl function in free form or esterified with a lower alcohol containing from 1 to 6 carbon atoms; - R' is a hydroxyl group or an ester group of formula: in which R 1 denotes a linear or branched, saturated or unsaturated aliphatic chain containing from 1 to 18 carbon atoms; b) at least one antiperspirant aluminium salt or complex; and c) at least one sequestrant chosen from amino acid-N,N-diacetic acid salts.