Multilayer polymer structures comprising a layer (A) based on at least one halohydrocarbon polymer linked to a layer (C) based on at least one olefin polymer via a layer (B) containing from 100% to 10% by weight of at least one grafted olefin polymer and from 0 to 90% by weight of at least one halohydrocarbon polymer, the grafted olefin polymer being obtained by grafting a polymerizable monomer, a functional oligomer or a functional telomer onto a preactivated olefin polymer; process for obtaining them and use thereof.