A process for rolling tubes, in which two grooved rolls mounted opposite one another in a roll stand are moved back and forth, i.e., reciprocated, on tube-shaped rolling material, which is arranged on a tapered rolling mandrel supported in the axial direction by a mandrel bar. The rotary-driven rolls have, on their circumferential surfaces, narrowing work grooves matching in shape to the tapered rolling mandrel, which roll down the rolling material on the rolling mandrel. At the ends of the work passes the rolls release the rolling material at the two dead centers of the roll stand path so as to assist in the advancement and rotation of the rolling material. According to the invention, the tube-shaped rolling material and the rolling mandrel are driven asynchronously in the same rotational direction at different rotational speeds.