A process for making a composite tube uniquely suited for use in ethylene pyrolysis furnaces wherein the tube comprises an outer shell made from a wrought or cast Fe—Ni—Cr heat resistant alloy and an inner core made from INCOLOY® alloy MA956 powder. The outer shell and powder core are heated and simultaneously extruded to form a composite tube. The process is carried out at temperature, and time at temperature, preferably less than 1200° C. so as to prevent recrystalization of the very fine grain structure in the alloy MA956. This un-recrystalized fine grain structure permits pilgering and/or cold drawing of the extruded composite tube to final size. The composite tube provided by the present invention is uniquely suited for use in the petrochemical and chemical process industries, so as to increase the efficiency and productivity of their respective processes. The thin core layer of alloy MA956 provides high resistance to carburization and coke formation heretofore caused by the hydrocarbon feedstock flowing through the composite tube, while the outer shell of Fe—Ni—Cr heat resistant alloy provides overall strength and rigidity to the tube. The use of the outer shell in the composite tube also solves the joining problem heretofore encountered in joining alloy MA956. A root pass or passes using an alloy MA956 filler metal followed by overlay welding passes using a filler metal compatible with the heat resistant alloy, such as INCONEL alloy 617 or FM 25/35, joins the outer shells of adjoining composite tubes and, thus, solves the welding problem.