Method for the continuous production of a composite pipe consisting of a smooth internal pipe and an external pipe, provided with elevations, welded thereto, the composite pipe comprising a pipe socket and a central longitudinal axis, and the method comprising the following method steps: - extruding, concentrically to the central longitudinal axis, a thermoplastic external tube of plastic material into a mould moving in a direction of conveyance, the mould consisting of half shells (12, 12') abutting closely to each other in the direction of conveyance such as to form a pair, - providing the external tube with a corrugation comprising elevations and troughs (40, 40') in annular mould recesses (32, 32'), formed between annular webs (48, 49, 54), of the pairs of half shells (12, 12') as a result of a pressure difference acting from the inside to the outside; - extruding, concentrically to the central longitudinal axis, a thermoplastic internal tube of plastic material into the external tube and onto a calibrating mandrel in a direction downstream of the external tube relative to the direction of conveyance; - welding the internal tube to the troughs (40, 40') of the external tube in gaps formed between the annular webs (48, 49, 54) and the calibrating mandrel; - widening the external tube in predetermined distances by applying a pressure difference acting from the inside to the outside so as to produce a pipe socket; - applying a gas having a pressure above atmospheric pressure to the internal tube from inside and pressing the internal tube, which is being widened at the same time, against the widened portion of the external tube such as to achieve a full surface-to-surface contact in order to complete the pipe socket, and - forming, between the pipe socket and the nearest trough arranged upstream thereof in the direction of conveyance, a transition portion protruding in an obliquely outward direction relative to the central longitudinal axis, the transition portion being formed of the internal tube and the external tube, wherein during the formation of the transition portion, the internal tube is pressed against the already widened external tube, characterized in that the internal tube and the external tube are squeezed against each other in the gaps, and that in the squeezed portions between the internal tube and the external tube, the width a of the first trough arranged closest to the transition portion in the direction of conveyance is made greater than the width b of the second troughs arranged upstream of the first trough in the direction of conveyance. - extruding, concentrically to the central longitudinal axis, a thermoplastic external tube of plastic material into a mould moving in a direction of conveyance, the mould consisting of half shells (12, 12') abutting closely to each other in the direction of conveyance such as to form a pair, - providing the external tube with a corrugation comprising elevations and troughs (40, 40') in annular mould recesses (32, 32'), formed between annular webs (48, 49, 54), of the pairs of half shells (12, 12') as a result of a pressure difference acting from the inside to the outside; - extruding, concentrically to the central longitudinal axis, a thermoplastic internal tube of plastic material into the external tube and onto a calibrating mandrel in a direction downstream of the external tube relative to the direction of conveyance; - welding the internal tube to the troughs (40, 40') of the external tube in gaps formed between the annular webs (48, 49, 54) and the calibrating mandrel; - widening the external tube in predetermined distances by applying a pressure difference acting from the inside to the outside so as to produce a pipe socket; - applying a gas having a pressure above atmospheric pressure to the internal tube from inside and pressing the internal tube, which is being widened at the same time, against the widened portion of the external tube such as to achieve a full surface-to-surface contact in order to complete the pipe socket, and - forming, between the pipe socket and the nearest trough arranged upstream thereof in the direction of conveyance, a transition portion protruding in an obliquely outward direction relative to the central longitudinal axis, the transition portion being formed of the internal tube and the external tube, wherein during the formation of the transition portion, the internal tube is pressed against the already widened external tube,