The invention relates to an axial thread rolling head, comprising a head part, in which at least three thread rolls are rotatably mounted, wherein the thread rolls among themselves border an insertion section for a workpiece and wherein the thread rolls each have a profile for forming an outer thread on the workpiece, wherein the thread rolls are held non-adjustably in the radial direction in the head part, wherein the profile of the thread rolls is respectively designed asymmetrically such that the thread rolls with their asymmetrical profile form a symmetrical external thread on the workpiece. The invention also relates to a corresponding method.