Topically applicable dermocosmetic compositions for combating the clinical signs of skin aging and/or for improving the appearance of the skin, the scalp or the hair, comprise an anti-free-radical effective amount of at least one novel melatonin derivative having the structural formula (I): ##STR1## in which R.sub.1 is a lower alkyl radical, R.sub.2 is a hydrogen atom or a lower alkyl radical, and R.sub.3 is a hydrogen atom or a lower acyl radical, with the proviso that the hydroxyl radical is in the 4-, 6- or 7-position on the indole ring system, or a physiologically acceptable salt, solvate or bioprecursor/prodrug thereof, formulated into a topically applicable, cosmetically/dermatologically acceptable vehicle, carrier or diluent therefor.