The present invention relates to the use of a known compound as an agent for promoting and/or accelerating fibroblast proliferation and/or differentiation and, consequently, cicatrization. This compound is a copolymer of a 2-methyl-2-[(1-oxo-2-propenyl)amino]-1-propanesulphonic acid salt and of propenoic acid 2-hydroxyethyl ester. It may be used alone or in combination with other active substances for inducing or accelerating cicatrization. This compound, alone or in combination with another active substance, may be administered directly on the wound and the surrounding area or the mucous membranes, by topical application. It may also be used ex vivo, in particular for generating cells for skin grafts.
