A method for producing a biaxially oriented tube from thermoplastic material, wherein a tube in preform condition is extruded from thermoplastic material using an extruder which is provided with an extruder die head having an inner die member, the inner die member forming a lumen in the tube in preform condition, wherein the tube in preform condition is subjected to a temperature conditioning by one or more tempering devices so that a tempered tube is obtained having an orientation temperature which is suitable for the thermoplastic material, and wherein use is made of an expansion device in the lumen downstream of the extruder, said expansion device comprising: - a non-deformable expansion part having a gradually increasing diameter to a maximum diameter at a downstream end thereof, which expansion part is contacted by the tube and exerts an expanding force on the tube so as to bring about expansion of the tempered tube in circumferential direction, - a run-off part adjoining the expansion part at the downstream end thereof, wherein the method comprises drawing the tempered tube over the expansion device using a drawing device which is arranged downstream of the expansion device and acts on the tube, in such a manner that said tube is drawn over the expansion device and transformed from a tube in preform condition into a biaxially oriented tube with thermoplastic material being oriented in axial direction and in circumferential direction, wherein said biaxially oriented tube is cooled, wherein the run-off part of the expansion device has a reduced diameter section having a smaller diameter than the maximum diameter of the expansion part, and in that use is made of at least one outer diameter ring member (90,91) that is arranged at the location of the reduced diameter section of the run-off part of the expansion device and around said reduced diameter section, and in that the run-off part comprises an increased diameter portion (20c1) - downstream of the one or more outer diameter ring members (90,91) and delimiting the downstream end of the reduced diameter section of the run-off part - said increased diameter portion having a greater diameter than said reduced diameter section, preferably said increased diameter portion being non-deformable, and wherein the oriented tube sealingly engages the expansion device in a region at or near the maximum diameter of the expansion part and sealingly engages the increased diameter portion (20c1) and a fluid volume is present between the reduced diameter section of the run-off part and the oriented tube, wherein a pressurized gas is introduced in the fluid volume between the reduced diameter section of the run-off part and the oriented tube, and in that the oriented tube passes through the at least one outer diameter ring member (90,91) while being in contact with said at least one outer diameter ring member, wherein the at least one outer diameter ring member (90,91) is embodied as a constrictive outer diameter ring member, said ring member exerting a radial constrictive force on the oriented tube passing there through, thereby, at least during the passage through the ring member, reducing the outer diameter of the oriented tube, and in that the outer diameter ring member (90,91) and the reduced diameter section are dimensioned such that seizing of the oriented tube between the run-off part and the at least one outer diameter ring member is avoided, the inside of the oriented tube being radially spaced from the reduced diameter section, and in that the oriented tube is cooled externally while passing over the run-off part by a first external cooling device, the method being characterized in that J Z use is made of an upstream outer diameter ring member and a downstream outer diameter ring member, the upstream and downstream outer ring members being arranged spaced apart in series at the location of the reduced diameter section of the run-off part and around said reduced diameter section, the oriented tube passing through said ring members, preferably the first external cooling device cooling the stretch of oriented tube between the ring members (90,91). - a non-deformable expansion part having a gradually increasing diameter to a maximum diameter at a downstream end thereof, which expansion part is contacted by the tube and exerts an expanding force on the tube so as to bring about expansion of the tempered tube in circumferential direction, - a run-off part adjoining the expansion part at the downstream end thereof,