The present invention relates to a multilayer structure based on rubber and on polyamide-block graft copolymer, comprising in succession: a) optionally a first, inner layer (1) formed of a rubber or of a polyamide, b) at least one layer (2) based on a polyamide-block graft copolymer composed of a polyolefin backbone and at least one polyamide graft, wherein the grafts are attached to the backbone by the residues of an unsaturated monomer (X) having a function which is capable of reacting with an amine-terminated polyamide, the residues of the unsaturated monomer (X) being attached to the backbone by grafting or copolymerization via its double bond, c) a second layer (3) formed of a rubber, d) optionally a binder layer (4), e) an outer layer (5) formed of a rubber, f) optionally a reinforcing layer situated between two of the preceding layers or within said layers. One advantageous use of this structure relates to tubes for transporting refrigerant fluids of CO2 or HFA type in conditioned-air circuits, more particularly for automobiles, and the transport of automobile engine cooling liquids.