The means for making a bimetallic pipe, made up of a pipe telescopically inserted with clearance inside a pipe and projecting from both ends of the latter, comprising a fixed expansion head and a moveable expansion head, wherein the ends of the bimetallic pipe are inserted before proceeding to the hydraulic or oil hydraulic closure of particular clamping members around each end of the outer pipe while the inner pipe has the ends positioned against the corresponding elastic abutments made inside each of the above-mentioned heads, thus being free to move axially and radially to rotate around its own axis during plastic expansion thereof.