The invention concerns the use of compounds of formula (I) R-N1-spermidine, or 1,4-butandiamine,N-(3-amino propyl)-N1—R, (I) H2N—(CH2)3—N1 (R)—(CH2)4—NH2, as such or in the form of pharmaceutically acceptable derivatives, as the active principle in a pharmaceutical or cosmetic composition to preserve and protect epithelial stem cells, and progenitor cells that derive from them, through topical application on the skin or through the use of compounds in cell cultures. Hence, the invention especially concerns the use of compounds of formula (I) to treat cicatricial alopecia, and to stimulate and accelerate tissue repair and healing of both wounds and epidermal scars.