FIELD: processes for cold pilger rolling, namely of superthin-wall tubes and small-diameter rods. SUBSTANCE: method is realized in apparatus having rolls mounted in mill for cold pilger rolling having rolling stand performing reciprocation motion. Rolls are narrowed and sized by their perimeter. By means of said rolls rolled product is turned at least in one of two dead points of rolling stand and it is transported forward. In order to rotate rolled product and to transport it forward, transporting apparatus is mounted at outlet side directly after rolling stand for embracing along perimeter article rolled in pilger rolling mill. In order to control transportation speed of transporting apparatus arranged at outlet side, at first transportation speed of rolled product at outlet of rolling stand is measured when transporting apparatus is open at outlet side. Measurement result is used for controlling speed of drive mechanism of transporting apparatus in such a way that to increase speed of transporting apparatus arranged at outlet side by 3 - 10% relative to transportation speed of drive mechanism for feeding at inlet side before closing transporting apparatus relative to rolled product. EFFECT: possibility for rolling superthin-wall tubes, especially small tubes or small-diameter rods without hazard of occurring jamming or laps. 6 cl, 1 dwg, 1 ex
