Cosmetic skin or hair compositions are provided comprising a combination of (A) a dialkyl carbonate of the formula R.sup.1 OC(O)OR.sup.2 wherein R.sup.1 and R.sup.2 are a linear or branched C.sub.6-22 alkyl group and (B) an aminoalkyl amide of the formula R.sup.3 CONH(CH.sub.2).sub.n --NR.sup.4 R.sup.5 wherein R.sup.3 CO is a linear C.sub.6-22 acyl group, R.sup.4 and R.sup.5 are selected from the group consisting of alkyl, hydroxyalkyl and aminoalkyl groups containing up to 6 carbon atoms or R.sup.4 and R.sup.5 together with the N atom form a 5- or 6-membered ring and n is a number from 2 to 6.