In at least one method for manufacturing a double-walled, thermoplastic tube with a connecting sleeve, which enables precise and complete moulding of the connecting sleeve by simple means, it is provided that a) a first tube (1) is extruded into a mould tunnel (4) comprising at least one row of moulds (5) guided on a path, b) the first tube (1) is given a corrugated shape in at least one first section and expanded into a connecting sleeve in at least one second section, c) a second tube (6) is extruded into the first tube and pressed against the corrugation troughs (8) of the first tube (1), d) while the first tube (1) is being given a corrugated shape and the second tube (6) extruded into the first, the space (A) between the two tubes (1, 6) is subjected to a pressure p1 that is above atmospheric pressure, e) the space (A) between the two tubes (1, 6) is subjected, at a specified time before or after expansion of the first tube (1) into a connecting sleeve, to an essentially constant pressure p2≦p1 above atmospheric pressure, or to a variable, but not continuously declining pressure p2, f) during extrusion of the second tube (6) into the first tube (1), which has already been expanded into a connecting sleeve, the second tube (6) is internally subjected to a pressure p3 above atmospheric pressure and pressed against the first tube (1), and g) pressure p1 is subsequently again applied to space (A) between the two tubes.