Aqueous dispersion, characterized in that it comprises 1) at least one vinylidene chloride polymer and 2) at least one random, alternating or gradient copolymer consisting of a) at least one monomer unit (m 1) carrying at least one phosphonate group -PO (OR 1) with R 1 being a hydrogen atom or an alkyl radical comprising from 1 to 11 carbon atoms, and b) monomer units which represent at least 50 % by weight of the copolymer, derived from at least one monomer chosen from styrene, maleic anhydride, itaconic acid and the (meth)acrylic monomers corresponding to the general formula: CH 2 =CR 2 R 3 in which R 2 is chosen from hydrogen and the methyl radical and R 3 is chosen from the -CN radical and the -CO-R 4 radical in which R 4 is chosen from the -OH radical, the -O-R 5 radicals with R 5 chosen from the linear or branched alkyl radicals comprising from 1 to 18 carbon atoms which optionally carry one or more -OH radicals, the epoxyalkyl radicals comprising from 2 to 10 carbon atoms and the alkoxyalkyl radicals comprising a total of 2 to 10 carbon atoms and finally R 4 is also chosen from the -NR 6 R 7 radicals in which R 6 and R 7, which are identical or different, are chosen from hydrogen and the alkyl radicals comprising from 1 to 10 carbon atoms which optionally carry one or more -OH radicals; and optionally c) monomer units different from monomer units and and from monomer units derived from vinylidene chloride. 1) at least one vinylidene chloride polymer and 2) at least one random, alternating or gradient copolymer consisting of a) at least one monomer unit (m 1) carrying at least one phosphonate group -PO (OR 1) with R 1 being a hydrogen atom or an alkyl radical comprising from 1 to 11 carbon atoms, and b) monomer units which represent at least 50 % by weight of the copolymer, derived from at least one monomer chosen from styrene, maleic anhydride, itaconic acid and the (meth)acrylic monomers corresponding to the general formula: CH 2 =CR 2 R 3 in which R 2 is chosen from hydrogen and the methyl radical and R 3 is chosen from the -CN radical and the -CO-R 4 radical in which R 4 is chosen from the -OH radical, the -O-R 5 radicals with R 5 chosen from the linear or branched alkyl radicals comprising from 1 to 18 carbon atoms which optionally carry one or more -OH radicals, the epoxyalkyl radicals comprising from 2 to 10 carbon atoms and the alkoxyalkyl radicals comprising a total of 2 to 10 carbon atoms and finally R 4 is also chosen from the -NR 6 R 7 radicals in which R 6 and R 7, which are identical or different, are chosen from hydrogen and the alkyl radicals comprising from 1 to 10 carbon atoms which optionally carry one or more -OH radicals; and optionally c) monomer units different from monomer units and and from monomer units derived from vinylidene chloride. a) at least one monomer unit (m 1) carrying at least one phosphonate group -PO (OR 1) with R 1 being a hydrogen atom or an alkyl radical comprising from 1 to 11 carbon atoms, and b) monomer units which represent at least 50 % by weight of the copolymer, derived from at least one monomer chosen from styrene, maleic anhydride, itaconic acid and the (meth)acrylic monomers corresponding to the general formula: CH 2 =CR 2 R 3