Anhydrous composition in aerosol form containing: i) an oily phase comprising, in a physiologically acceptable medium: - one or more volatile oils, - one or more antiperspirant active agents chosen from aluminium and/or zirconium salts, and - one or more water-insoluble film-forming block ethylenic polymers comprising a first block with a glass transition temperature (Tg) of greater than or equal to 85°C and a second block with a Tg of less than or equal to 20°C, and ii) one or more propellants; the said oily phase containing less than 15% by weight and even more preferably less than 12% by weight of non-volatile polydimethylsiloxane relative to the total weight of the oils, the said second block comprising at least one monomer with a Tg of less than or equal to 20°C, chosen from the following monomers, alone or as a mixture: - the acrylates of formula CH 2 =CHCOOR 3, with R 3 representing a linear or branched C 1 to C 12 alkyl group, with the exception of the tert-butyl group, in which one or more heteroatoms chosen from O, N and S are optionally intercalated, the said alkyl group also possibly being substituted with one or more substituents chosen from hydroxyl groups and halogen atoms; - the methacrylates of formula CH 2 =C(CH 3)-COOR 4, with R 4 representing a linear or branched C 6 to C 12 alkyl group in which one or more heteroatoms chosen from O, N and S are optionally intercalated, the said alkyl group also possibly being substituted with one or more substituents chosen from hydroxyl groups and halogen atoms; - the vinyl esters of formula R 5 -CO-O-CH=CH 2 in which R 5 represents a linear or branched C 4 to C 12 alkyl group; - C 4 to C 12 alkyl vinyl ethers; - N-(C 4 to C 12)alkyl acrylamides; - the monomers of formula below, alone or as a mixture: in which: - R 1 is a hydrogen atom or a methyl radical; - Z is a divalent group chosen from -COO-, -CONH-, -CONCH 3 -, -OCO-, -O-, -SO 2 - -CO-O-CO- and -CO-CH 2 -CO-; - x is 0 or 1; - R 2 is a linear, branched or cyclic, saturated or unsaturated, optionally aromatic divalent carbon-based radical, of 1 to 30 carbon atoms, which may comprise 1 to 18 heteroatoms chosen from O, N, S, F, Si and P; - m is 0 or 1; - n is an integer between 3 and 300 inclusive; - R 3 is a hydrogen atom or a linear, branched or cyclic, saturated or unsaturated, optionally aromatic carbon-based radical, of 1 to 30 carbon atoms, which may comprise 1 to 20 heteroatoms chosen from O, N, S, F, Si and P. i) an oily phase comprising, in a physiologically acceptable medium: - one or more volatile oils, - one or more antiperspirant active agents chosen from aluminium and/or zirconium salts, and - one or more water-insoluble film-forming block ethylenic polymers comprising a first block with a glass transition temperature (Tg) of greater than or equal to 85°C and a second block with a Tg of less than or equal to 20°C, and - one or more volatile oils, - one or more antiperspirant active agents chosen from aluminium and/or zirconium salts, and - one or more water-insoluble film-forming block ethylenic polymers comprising a first block with a glass transition temperature (Tg) of greater than or equal to 85°C and a second block with a Tg of less than or equal to 20°C, and ii) one or more propellants; - the acrylates of formula CH 2 =CHCOOR 3, with R 3 representing a linear or branched C 1 to C 12 alkyl group, with the exception of the tert-butyl group, in which one or more heteroatoms chosen from O, N and S are optionally intercalated, the said alkyl group also possibly being substituted with one or more substituents chosen from hydroxyl groups and halogen atoms; - the methacrylates of formula CH 2 =C(CH 3)-COOR 4, with R 4 representing a linear or branched C 6 to C 12 alkyl group in which one or more heteroatoms chosen from O, N and S are optionally intercalated, the said alkyl group also possibly being substituted with one or more substituents chosen from hydroxyl groups and halogen atoms; - the vinyl esters of formula R 5 -CO-O-CH=CH 2 in which R 5 represents a linear or branched C 4 to C 12 alkyl group; - C 4 to C 12 alkyl vinyl ethers; - N-(C 4 to C 12)alkyl acrylamides; - the monomers of formula below, alone or as a mixture: in which: - R 1 is a hydrogen atom or a methyl radical; - Z is a divalent group chosen from -COO-, -CONH-, -CONCH 3 -, -OCO-, -O-, -SO 2 - -CO-O-CO- and -CO-CH 2 -CO-; - x is 0 or 1; - R 2 is a linear, branched or cyclic, saturated or unsaturated, optionally aromatic divalent carbon-based radical, of 1 to 30 carbon atoms, which may comprise 1 to 18 heteroatoms chosen from O, N, S, F, Si and P; - m is 0 or 1; - n is an integer between 3 and 300 inclusive; - R 3 is a hydrogen atom or a linear, branched or cyclic, saturated or unsaturated, optionally aromatic carbon-based radical, of 1 to 30 carbon atoms, which may comprise 1 to 20 heteroatoms chosen from O, N, S, F, Si and P. - R 1 is a hydrogen atom or a methyl radical; - Z is a divalent group chosen from -COO-, -CONH-, -CONCH 3 -, -OCO-, -O-, -SO 2 - -CO-O-CO- and -CO-CH 2 -CO-; - x is 0 or 1; - R 2 is a linear, branched or cyclic, saturated or unsaturated, optionally aromatic divalent carbon-based radical, of 1 to 30 carbon atoms, which may comprise 1 to 18 heteroatoms chosen from O, N, S, F, Si and P; - m is 0 or 1; - n is an integer between 3 and 300 inclusive; - R 3 is a hydrogen atom or a linear, branched or cyclic, saturated or unsaturated, optionally aromatic carbon-based radical, of 1 to 30 carbon atoms, which may comprise 1 to 20 heteroatoms chosen from O, N, S, F, Si and P.