The invention relates to the use of para-coumaric acid or para-hydroxycinnamic acid derivatives in cosmetic or dermatological compositions, specifically to the use of at least one compound derived from para-coumaric acid having a general formula (I) below: in which, especially, Z represents an oxygen or an —NH— group; X and Y are identical and each represent a CH or CH2 group, as an active principle with depigmenting, free-radical-scavenging and/or antiinflammatory activity. The invention also relates to the use of the above compounds for cosmetic care or for the preparation of a pharmaceutical composition, especially for depigmenting an area of skin, having antiradical and/or antiinflammatory activity.