6-tert-Butyl-1,1-dimethylindane derivatives which are unsaturated in the 4-position of formula: X represents: (i) either a radical of formula: and Y represents a radical of formula: (ii) or a radical of formula: and Y represents either a radical of formula (b) or a radical of formula: Z being —O—, —S— or R1 represents —CH3, —(CH2)p—OR4, —(CH2)p—COR5 or —S(O)t—R6, p being 0, 1, 2 or 3, t being 0, 1 or 2, R2 represents H or lower alkyl, R3 represents H, lower alkyl or —COR7, R4 represents H, lower alkyl, —COR7, aryl, aralkyl, mono- or polyhydroxyalkyl, or a polyether radical, R5 represents H, lower alkyl, —OR8 or —N(r′)(r″), R6 represents H or lower alkyl, R7 represents lower alkyl, R8 represents H, alkyl, alkenyl, alkynyl, aryl, aralkyl, mono- or polyhydroxyalkyl, a sugar residue or an amino acid residue, r′ and r″ represent H, lower alkyl, —COR7, aryl, a sugar residue or an amino acid residue or r′ and r″ form a heterocycle, and the salts of the compounds of formula (I). Use in the topical and systemic treatment of dermatological conditions, as well as in cosmetics.