An assembly for production of a threaded connection, including a first and a second tubular component with an axis of revolution and each including at one of its ends at least one first threaded zone produced on an external or internal peripheral surface of the component depending on whether the threaded end is male or female in type, and capable of cooperating together on makeup, the ends finishing in a terminal surface. At least one of the threaded zones has, in longitudinal section passing through the axis, a profile that follows a continuous and concave portion of a curve over at least 10% of the length of engaged threads of the threaded zone.