Peptide compounds of the following general formula (I): R1-(AA)n-X1-X2-X3-Lys-Lys-Gln-Lys-Trp-X4-(AA)p-R2 are disclosed herein. The peptide compounds can be used as Telomeric repeat-binding factor 2 (TRF2) protein-modulating compounds and have a preventive action on deoxyribonucleic acid (DNA) double-strand breaks. In addition, cosmetic compositions that include at least one peptide of general formula (I) in a physiologically acceptable medium are disclosed along with methods for preventing and/or treating cutaneous signs of aging and photoaging.