Process for chemically modifying a polymer matrix chosen from matrices made of fluoropolymers presenting no aromatic group in the main chain or in the side chains and matrices made of aliphatic polymers comprising several units, identical or different, of formula: -C(R 1)(R 2)-C(R 3)(R 4)- in which the groups R 1, R 2, R 3 and R 4 identical or different, are chosen from a hydrogen, a halogen, an optionally substituted alkyl group having 1 to 6 carbon atoms and an optionally substituted heteroalkyl group having 1 to 6 carbon atoms, a nitro group, a cyano group, an amine group, a carboxylic acid group, a sulfonic acid group, an amide group, an ester group, an imide group and an ether group, characterized in that said process comprises the steps consisting in: a 1) irradiating, under inert gas that does not absorb at the irradiation wavelength, said matrix with UV light having a wavelength of less than 300 nm by using a V-UV excimer lamp where V-UV represents a subband of UV-C from 200 to 100 nm or with laser irradiations carried out with a Nd:YAG pulsed laser operating at 266 nm, in order to generate, at a distance greater than 250 nm, zones that have short polymer chains, formed by scission of the existing chains during the passage of the UV radiation and that have free radicals denoted hereinbelow as "activated zones"; and b 1) bringing said irradiated matrix only presenting radicals of alkyl type, obtained in step (a 1) into contact with at least one compound bearing at least one ethylenically unsaturated group, said solution being subjected to a sparging under nitrogen prior to said contacting and from this contacting onwards, and inducing the grafting by radical reaction in the polymer matrix of at least one unit derived from the compound bearing an ethylenically unsaturated group and advantageously several units of the (or of different) compound(s) bearing an ethylenically unsaturated group brought into the presence of the irradiated polymer matrix, the first of these units being bonded to the polymer matrix by a covalent bond involving an atom of said matrix and an atom of said unit. a 1) irradiating, under inert gas that does not absorb at the irradiation wavelength, said matrix with UV light having a wavelength of less than 300 nm by using a V-UV excimer lamp where V-UV represents a subband of UV-C from 200 to 100 nm or with laser irradiations carried out with a Nd:YAG pulsed laser operating at 266 nm, in order to generate, at a distance greater than 250 nm, zones that have short polymer chains, formed by scission of the existing chains during the passage of the UV radiation and that have free radicals denoted hereinbelow as "activated zones"; and b 1) bringing said irradiated matrix only presenting radicals of alkyl type, obtained in step (a 1) into contact with at least one compound bearing at least one ethylenically unsaturated group, said solution being subjected to a sparging under nitrogen prior to said contacting and from this contacting onwards, and inducing the grafting by radical reaction in the polymer matrix of at least one unit derived from the compound bearing an ethylenically unsaturated group and advantageously several units of the (or of different) compound(s) bearing an ethylenically unsaturated group brought into the presence of the irradiated polymer matrix, the first of these units being bonded to the polymer matrix by a covalent bond involving an atom of said matrix and an atom of said unit.