Heat-shrinkable multilayer films having a surface layer based on at least one olefinic polymer and/or copolymer, a layer based on a mixture of an ionomer having a maximum MFI of 4 dg/min and an ionomer having an MFI>4 dg/min, a barrier layer based on polyvinylidene chloride or a vinylidene chloride polymer, a layer based on the ionomer mixture or an olefinic copolymer, and a sealing layer of at least one polyolefin or olefinic copolymer.