Method for the continuous production of a thermally insulated line pipe by means of a production plant, wherein the thermally insulated line pipe comprises, in the finished state, an outer pipe made of LLD-PE or LLD-PE-containing plastic, at least one inner pipe arranged in the outer pipe and a hardened insulating foam between the inner pipe and the outer pipe, wherein the production of the thermally insulated line pipe is carried out in a substantially horizontal production direction x through various stations of the production plant, wherein the method comprises the steps of a) forming a foil tube around the at least one inner pipe and introducing a foamable starting material into the foil tube, which starting material expands to form an insulating foam and the insulating foam hardens, wherein the hardened insulating foam fills at least part of the space between the inner pipe and the outer pipe in the finished line pipe, b) passing the inner pipe with the foil tube and the foamable starting material through an extrusion head, by means of which the outer pipe is extruded around the inner pipe with the foil tube, so that a semi-finished product is formed, c) forming a corrugation of the outer pipe in a corrugator to produce a corrugated outer pipe, wherein the foamable starting material is formed before being introduced into the foil tube in such a way that it essentially only begins to expand when the semi-finished product emerges from the corrugator, thereby forming a foam front, characterized by the steps of d) detecting a position of the longitudinal axis of the corrugated outer pipe relative to the position of the longitudinal axis of the at least one inner pipe by means of a detection device, e) in the event that in step d) the longitudinal axes are not arranged in an intended position relative to one another, adjusting the position of the corrugated outer pipe relative to the inner pipe by means of a positioning device until its longitudinal axis is arranged in the intended position relative to the longitudinal axis of the inner pipe, f) fix the outer pipe in the intended position. a) forming a foil tube around the at least one inner pipe and introducing a foamable starting material into the foil tube, which starting material expands to form an insulating foam and the insulating foam hardens, wherein the hardened insulating foam fills at least part of the space between the inner pipe and the outer pipe in the finished line pipe, b) passing the inner pipe with the foil tube and the foamable starting material through an extrusion head, by means of which the outer pipe is extruded around the inner pipe with the foil tube, so that a semi-finished product is formed, c) forming a corrugation of the outer pipe in a corrugator to produce a corrugated outer pipe, wherein the foamable starting material is formed before being introduced into the foil tube in such a way that it essentially only begins to expand when the semi-finished product emerges from the corrugator, thereby forming a foam front, characterized by the steps of wherein the foamable starting material is formed before being introduced into the foil tube in such a way that it essentially only begins to expand when the semi-finished product emerges from the corrugator, thereby forming a foam front, characterized by the steps of d) detecting a position of the longitudinal axis of the corrugated outer pipe relative to the position of the longitudinal axis of the at least one inner pipe by means of a detection device, e) in the event that in step d) the longitudinal axes are not arranged in an intended position relative to one another, adjusting the position of the corrugated outer pipe relative to the inner pipe by means of a positioning device until its longitudinal axis is arranged in the intended position relative to the longitudinal axis of the inner pipe, f) fix the outer pipe in the intended position.