A PVC-free multilayer tube, preferably for medical purposes, with more dependable peelability, comprises at least three layers, of which a base layer comprising a first plastics material has been bonded to at least one connection layer comprising a second plastics material by means of at least one buffer layer arranged between the base layer and the at least one connection layer, the buffer layer comprising a third plastics material, wherein the multilayer tube can be used to mold a coil or a loop with a diameter of down to 50 mm without undesirable kinking. Each of the first and second plastics materials is comprised of at least 25% by weight, based on the total weight of the base layer and the connection layer, respectively, of polyolefins, while the third plastics material has a proportion, based on the total weight of the buffer layer, of more than 75% by weight of a thermoplastic elastomer which is not a polyolefin.