A cosmetic composition for skin and/or hair, which comprises at least one kind of substance selected from the group consisting of an N.sup..alpha.,N.sup.G-di-acylarginine, for example, a compound represented by the following general formula (I): ##STR00001## wherein R.sup.1 and R.sup.2 each independently represents a straight or branched-chain alkyl group having 1 to 21 carbon atoms or a straight or branched-chain alkenyl group having 2 to 21 carbon atoms. The cosmetic composition imparts much moistness and superior conditioning effects such as body or elasticity to hair, and to skin, said composition does not impart tackiness and blocked feeling, whilst imparts superior feeling of use such as moistness.