FIELD: mechanical engineering. SUBSTANCE methods for the production of machine parts of the screw type, manufactured on lathes. A method for manufacturing a body of revolution with an external thread on a CNC lathe equipped with a through-cutting tool and a whirling thread-cutting head consists in making the workpiece rotate relative to the Z-axis of the machine in the positive direction and linearly moving the through-cutting tool interacting with it along the Z-axis of the machine in the negative direction. Then there is a retraction of the through cutter from the surface of the workpiece in a positive direction along the X axis of the lathe. Rotation is imparted to the whirling thread-cutting head. The cutters of the whirling head are brought in and cut into the surface of the workpiece, and the head moves linearly along the Z axis of the lathe. After the withdrawal of the through cutter and before the approach and plunge of the cutters of the head, the workpiece is given rotation in the negative direction. The linear movement of the whirling head is carried out along the Z-axis of the lathe in the positive direction. The approach and insertion of the cutters of the whirling head is carried out in the position of the end of the linear movement of the through cutter. The cessation of the movement of the head is carried out in the position of the beginning of the interaction of the through cutter with the surface of the workpiece. EFFECT: increased contact rigidity and increased versatility of the tool holder. 1 cl, 1 dwg.