The invention relates to a multilayer structure comprising the following successive layers: a polyamide or HDPE (high-density polyethylene) layer, a binder layer, a modified impact EVOH layer, possibly a binder layer, a polyamide or a mixture of polyamide and polyolefine or polyolefine layer which can contain charges, thereby making it antistatic. The modified impact EVOH layer is embodied in the form of a mixture based on EVOH and at least one type of modifier selected amongst: a) alkyl ethylene-(meth) acrylate functionalised copolymers, b) products obtained by a reaction (i) of an ethylene copolymer and an unsaturated graft or copolymerised with polyamide (ii) X monomer, c) a) and b) mixtures, d) polyamides, preferably PA 6, e) a) and d) mixtures, f) elastomers, preferably EPR, EPDM and NBR, which can be functionalised, g) S-B-M triblocs, h) triblocs consisting of a poly(butyl acrylate) bloc between two PMMA blocs, and I) S-B-S linear bloc or possibly star-shaped hydrogenated copolymers (then they are designated by S-EB-S).