Cosmetic composition which can be applied topically, comprising at least one compound of the general formula (I) in which R1 is H, C1-C20-alkyl, cycloalkyl or aryl-C1-C4-alkyl, n is 1-4, X is —O—, —NH— or —NR2— and R2H or C1-C20-alkyl; and at least one compound corresponding to the above formula (I) but in which XR1 with X having the possible meaning of —NH— is the residue of an alpha-amino acid; use of these compounds and of the composition for stimulating the synthesis of the proteins of the basement membrane; and also both those compounds of the formula (I) in which X is —NR2— and both R1 and R2 are different from H, and the compounds corresponding to formula (I) but in which XR1 with X having the possible meaning of —NH— is the residue of an alpha-amino acid, as such.