Composition in the form of a cosmetic formulation or dermatological medicament, suitable for maintaining skin cells at, or helping to restore skin cells to, their basal physiological state, enabling them to effect a regeneration of the dermis and the epidermis, comprising: --curcumin--a phosphosaccharide and possibly--a metal or basic oxide, or a biologically acceptable salt thereof, or a labile coordination compound thereof able to form, with at least one of said compounds: complexes, derivatives or associations which enhance their activity, in combination with excipients and/or diluents normally employed for cosmetic or pharmaceutical use.