The invention relates to a flame-proofed polymer composition that can be obtained form one or more α-olefin-vinyl acetate copolymers, having a vinyl acetate content of 40 to 90 wt %, relative to the total weight of the α-olefin vinyl acetate copolymers, and from a synergistic flame-proofing material combination, comprising, as component A, a phosphinic acid salt of the formula (I), where R1, R2 are C1-C6-alkyl, preferably C1-C4-alkyl, linear or branched; M is calcium, aluminium, zinc ions; m is 2 or 3; and, as component B, a metal hydroxide, preferably aluminium hydroxide (ATH).