Leukemia Inhibitory Factor (“LIF”), an LIF analogue, an LIF mimetic and a product capable of stimulating the expression of endogenous LIF, and mixtures thereof are useful, for (i) promoting the multiplication, in vitro, of a population of human skin stem cells and/or epidermal progenitors while maintaining them in an undifferentiated state, and/or for (ii) maintaining and/or increasing their capacity to generate a pluristratified epithelium, in particular a pluristratified epidermis and/or all or some of the skin appendages; also a library or a culture of human undifferentiated skin stem cells and/or epidermal progenitors is obtained in the presence of LIF, as are reconstructed epidermides and/or reconstructed skin, and kits for producing libraries of cells or reconstructed epidermides, and stem cells or reconstructed epidermides are prepared for the treatment of individuals exhibiting damaged skin (individuals suffering from third degree burns and individuals suffering from genetic diseases affecting the skin).