Abstract: The invention relates to a flame-proofed polymer composition that can be obtained from one or more ?-olefin/vinyl acetate copolymers, having a vinyl acetate content of 40 to 90 wt %, relative to the total weight of the ?-olefin/vinyl acetate copolymers, and from a synergistic flame-proofing material combination, containing, 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, aluminum, zinc ions; m is 2 or 3; and as component B, a metal hydroxide, preferably aluminum hydroxide (ATH); and, as component C, a melamine compound.