Method for reducing the cross-section of a tubular hollow body by forming the hollow body which has a hollow body wall made of a plastically deformable material and a hollow body axis running in the longitudinal direction of the hollow body , • wherein a forming die is arranged on the outer side of the hollow body and has a die opening designed for receiving the hollow body with an opening cross-section which is smaller than the hollow body cross-section of the hollow body in an initial state, • wherein a mandrel is arranged in the interior of the hollow body , • wherein the forming die arranged on the outer side of the hollow body is moved, with an axial movement of the die along the hollow body axis , in a direction of the axial movement of the die relative to the hollow body by means of a die drive with a cross-section of the hollow body being reduced, • wherein the hollow body is supported on an axial abutment fixed along the hollow body axis in the direction of the axial die movement during the axial die movement of the forming die arranged on the outside of the hollow body , • wherein the mandrel arranged inside the hollow body is moved along the hollow body axis through the die opening by means of a mandrel drive provided in addition to the die drive with an axial mandrel movement opposite the axial die movement of the forming die arranged on the outside of the hollow body , • wherein the hollow body wall is subjected to tensile stress due to the axial mandrel movement by means of the mandrel in a direction of the axial mandrel movement, and is thereby drawn through the die opening relative to the forming die arranged on the outside of the hollow body in the direction of the axial mandrel movement in that the mandrel is effectively supported against the hollow body wall in a force-fit in the direction of the axial mandrel movement, and • wherein the mandrel drive and the die drive are controlled in such a way that the axial mandrel movement and the axial die movement of the forming die arranged on the outside of the hollow body are superimposed on one another. • wherein a forming die is arranged on the outer side of the hollow body and has a die opening designed for receiving the hollow body with an opening cross-section which is smaller than the hollow body cross-section of the hollow body in an initial state, • wherein a mandrel is arranged in the interior of the hollow body , • wherein the forming die arranged on the outer side of the hollow body is moved, with an axial movement of the die along the hollow body axis , in a direction of the axial movement of the die relative to the hollow body by means of a die drive with a cross-section of the hollow body being reduced, • wherein the hollow body is supported on an axial abutment fixed along the hollow body axis in the direction of the axial die movement during the axial die movement of the forming die arranged on the outside of the hollow body , • wherein the mandrel arranged inside the hollow body is moved along the hollow body axis through the die opening by means of a mandrel drive provided in addition to the die drive with an axial mandrel movement opposite the axial die movement of the forming die arranged on the outside of the hollow body , • wherein the hollow body wall is subjected to tensile stress due to the axial mandrel movement by means of the mandrel in a direction of the axial mandrel movement, and is thereby drawn through the die opening relative to the forming die arranged on the outside of the hollow body in the direction of the axial mandrel movement in that the mandrel is effectively supported against the hollow body wall in a force-fit in the direction of the axial mandrel movement, and • wherein the mandrel drive and the die drive are controlled in such a way that the axial mandrel movement and the axial die movement of the forming die arranged on the outside of the hollow body are superimposed on one another. <EOS>