Composition in the form of an oil-in-water emulsion comprising, in a cosmetically acceptable medium: a) a continuous aqueous phase and b) an oily phase dispersed in the said aqueous phase and c) at least one water-insoluble block film-forming ethylenic polymer, the said polymer 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 d) at least one aluminium and/or zirconium antiperspirant salt or complex; wherein said first block with a Tg of greater than or equal to 85°C comprises at least one acrylate monomer of formula CH 2 =CH-COOR and at least one methacrylate monomer of formula CH 2 =C(CH 3)-COOR in which R, which may be identical or different, represents a C 4 to C 12 cycloalkyl group and preferably a C 8 to C 12 cycloalkyl; and wherein said second block with a Tg of less than or equal to 20°C comprises at least one monomer chosen, alone or as a mixture, from: - the acrylates of formula CH 2 =CHCOOR 3 in which R 3 represents a linear or branched C 1 to C 12 unsubstituted 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 methacrylates of formula CH 2 =C(CH 3)-COOR 4 in which R 4 represents a linear or branched C 6 to C 12 unsubstituted alkyl group, in which one or more heteroatoms chosen from O, N and S are optionally intercalated; - (meth)acrylic acid; and - the monomers of formula, preferably with x = 1 and Z=COO, 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. a) a continuous aqueous phase and b) an oily phase dispersed in the said aqueous phase and c) at least one water-insoluble block film-forming ethylenic polymer, the said polymer 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 d) at least one aluminium and/or zirconium antiperspirant salt or complex; - the acrylates of formula CH 2 =CHCOOR 3 in which R 3 represents a linear or branched C 1 to C 12 unsubstituted 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 methacrylates of formula CH 2 =C(CH 3)-COOR 4 in which R 4 represents a linear or branched C 6 to C 12 unsubstituted alkyl group, in which one or more heteroatoms chosen from O, N and S are optionally intercalated; - (meth)acrylic acid; and - the monomers of formula, preferably with x = 1 and Z=COO, - 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.