Vinylidene chloride copolymer composition characterized in that it comprises: (A) at least one vinylidene chloride copolymer which is a copolymer composed of vinylidene chloride in an amount of at least 50 wt % and of at least one comonomer at least one of which is chosen from (meth)acrylic monomers corresponding to the general formula: CH2═CR1R2, in which R1 is chosen from hydrogen and the methyl radical and R2 is the —CO—R3 radical in which R3 is the —O—R4 radical with R4 chosen from the linear or branched alkyl radicals containing from 1 to 18 carbon atoms optionally bearing one or more —OH radicals, the epoxyalkyl radicals containing from 2 to 10 carbon atoms and the alkoxyalkyl radicals containing a total of 2 to 10 carbon atoms; (B) from 0.5 to 4 parts by weight, per 100 parts by weight of (A), of epoxidized soybean oil; (C) from 0.01 to 2 parts by weight, per 100 parts by weight of (A), of at least one fluoropolymer chosen from the amorphous fluoropolymers for which the glass transition temperature is less than or equal to 200° C. and the semi-crystalline fluoropolymers for which the melting point is less than or equal to 200° C.; and (D) at most 1 part by weight, per 100 parts by weight of (A), of at least one acid scavenger. Process for preparing said composition. Multilayer film comprising said composition and packaging or bag formed from this film.