The invention provides a cosmetic composition for skin and/or hair care comprising one or more ß-aspartyl dipeptides, or oligomers thereof, or salts thereof, wherein each of said ß-aspartyl dipeptides comprises a ß-L-aspartyl moiety as the first amino acid residue. The invention further relates to a method for human skin and/or hair care, including anti-aging and/or anti-hair loss utilizing this composition.