A thermosetting composition, characterized in that it is devoid of any halogenated additive and of any halogenated structure in its components and in that it comprises: a) per 100 parts by weight of a resin, such weight being expressed as weight of dry resin, comprising: a1) at least one unsaturated polyester, having an acid number of less than 10, or a combination of a1) with a2) at least one vinyl ester resin, preferably selected from among the vinyl ester resins derived from epoxydized phenol-formaldehyde resins, b) 40 to 200 parts by weight of at least one reactive diluent selected from among the ethylenically unsaturated monomers copolymerizable with the said resin, c) 20 to 110 parts by weight of at least one agent for expansion by thermal decomposition, such agent being selected from among: melamine and derivatives thereof, guanidine, glycine, urea, triisocyanurates, azodicarbonamide, preferably from among melamine and its derivatives and more preferably melamine, d) 0 to 250 parts by weight of aluminium trihydrate, e) 10 to 80 parts by weight of at least one agent which is a precursor of charring selected from among; polyfunctional polyols sugars, starch, potato flour, pentaerythritol and/or derivatives of PET and/or erythritol and/or sorbitol, f) 50 to 200 parts of at least one compound from among: at least one phosphorus derivative and/or at least one boric acid derivative, g) optionally, at least one metal oxide, h) optionally, other additives and fillers, i) optionally, reinforcements based on natural fibres or synthetic fibres and corresponding fabrics, and in that said polyester a1) is based on an acid component composed of at least 60 mol% of maleic acid and/or anhydride and on a polyol component composed of at least 70 mol% of propylene glycol, with any remainder being selected from among dipropylene glycol and/or ethylene glycol and/or diethylene glycol and/or neopentyl glycol and/or 2-methylpropanediol and/or butanediols and/or pentanediols and/or hexanediols. a) per 100 parts by weight of a resin, such weight being expressed as weight of dry resin, comprising: a1) at least one unsaturated polyester, having an acid number of less than 10, or a combination of a1) with a2) at least one vinyl ester resin, preferably selected from among the vinyl ester resins derived from epoxydized phenol-formaldehyde resins, a1) at least one unsaturated polyester, having an acid number of less than 10, or a combination of a1) with a2) at least one vinyl ester resin, preferably selected from among the vinyl ester resins derived from epoxydized phenol-formaldehyde resins, b) 40 to 200 parts by weight of at least one reactive diluent selected from among the ethylenically unsaturated monomers copolymerizable with the said resin, c) 20 to 110 parts by weight of at least one agent for expansion by thermal decomposition, such agent being selected from among: melamine and derivatives thereof, guanidine, glycine, urea, triisocyanurates, azodicarbonamide, preferably from among melamine and its derivatives and more preferably melamine, d) 0 to 250 parts by weight of aluminium trihydrate, e) 10 to 80 parts by weight of at least one agent which is a precursor of charring selected from among; polyfunctional polyols sugars, starch, potato flour, pentaerythritol and/or derivatives of PET and/or erythritol and/or sorbitol, f) 50 to 200 parts of at least one compound from among: at least one phosphorus derivative and/or at least one boric acid derivative, g) optionally, at least one metal oxide, h) optionally, other additives and fillers, i) optionally, reinforcements based on natural fibres or synthetic fibres and corresponding fabrics,