A method for manufacturing a connection tube for connecting two tubes (8, 9) of different alloys, said connection tube having a first end portion and a second end portion, the method comprising the steps of: - forming a composite tube having an annular outer layer of a first alloy and an annular inner layer of a second alloy, - working a first end portion of the composite tube such that a diameter of the composite tube gradually decreases from a middle portion of the composite tube toward the first end portion, - removing the annular inner layer from the first end portion so that an inner diameter at the first end portion equals an inner diameter at the second end portion, characterised by - removing the annular outer layer from a second end portion of the composite tube, so that a middle portion extending between the first end portion and the second end portion has a larger wall thickness than each of the end portions (2, 3), thus forming a connection tube having a first end portion of said first alloy and a second end portion of said second alloy, and in that the step of forming a composite tube comprises the steps of: - providing an annular base component of the second alloy, wherein the annular base component has a central through-hole extending along a longitudinal axis of the annular base component, and wherein the annular base component has an externally threaded section, - providing an annular outer component of the first alloy, wherein the annular outer component has an internally threaded section configured to engage with the externally threaded section of the annular base component, - forming a tubular work piece by mounting the annular outer component around the annular base component such that the internally threaded section of the outer component is in engagement with the externally threaded section of the annular base component, forming a mechanical interlock between the threaded sections (302, 402), - hot working the work piece, so that on one hand a metallic bond is formed between the threaded sections (302, 402) of the annular outer component and the annular base component while the mechanical interlock is maintained, and so that on the other hand the work piece is elongated and an outer diameter of the tubular work piece is reduced, thus forming a composite tube; wherein the hot working step comprises extrusion. - forming a composite tube having an annular outer layer of a first alloy and an annular inner layer of a second alloy, - working a first end portion of the composite tube such that a diameter of the composite tube gradually decreases from a middle portion of the composite tube toward the first end portion, - removing the annular inner layer from the first end portion so that an inner diameter at the first end portion equals an inner diameter at the second end portion, characterised by - removing the annular outer layer from a second end portion of the composite tube, so that a middle portion extending between the first end portion and the second end portion has a larger wall thickness than each of the end portions (2, 3), thus forming a connection tube having a first end portion of said first alloy and a second end portion of said second alloy, and in that the step of forming a composite tube comprises the steps of: - providing an annular base component of the second alloy, wherein the annular base component has a central through-hole extending along a longitudinal axis of the annular base component, and wherein the annular base component has an externally threaded section, - providing an annular outer component of the first alloy, wherein the annular outer component has an internally threaded section configured to engage with the externally threaded section of the annular base component, - forming a tubular work piece by mounting the annular outer component around the annular base component such that the internally threaded section of the outer component is in engagement with the externally threaded section of the annular base component, forming a mechanical interlock between the threaded sections (302, 402), - hot working the work piece, so that on one hand a metallic bond is formed between the threaded sections (302, 402) of the annular outer component and the annular base component while the mechanical interlock is maintained, and so that on the other hand the work piece is elongated and an outer diameter of the tubular work piece is reduced, thus forming a composite tube; wherein the hot working step comprises extrusion.