A method for the extrusion of hose-shaped preforms which issue from a nozzle gap of an extrusion head delimited by a mandrel and a nozzle ring and are expanded in a blow mould into plastic barrels, which comprise a round cross section and a circumferential collar formed by upsetting, - wherein the nozzle gap width during the extrusion of the preforms is changed through an actuating movement of the mandrel and/or of the nozzle ring, - wherein the cross-sectional geometry of an elastically deformable sleeve arranged in the nozzle ring or on the mandrel and which delimits the nozzle gap on the circumference side is changed during the extrusion of the preforms either by two power drives located opposite, the actuating movements of which exert pulling forces and/or pressure forces on the sleeve arranged in the nozzle ring in a deformation axis orientated radially to the centre axis of the mandrel, or with a mandrelside arrangement of the sleeve by a vertically orientated power drive which is connected with radially acting actuating elements to the sleeve arranged on the mandrel, - wherein through actuating movements of at least one separately controlled additional element the circumference-side melt distribution in the sections of the preforms, which in the blow mould are expanded into an upper barrel termination and a barrel bottom, is influenced, - wherein the additional element acts on sections of the nozzle gap, which are assigned deformation-neutral regions of the elastically deformable sleeve, which are arranged substantially at 45° to the main deformation axis and during a deformation of the sleeve under the effect of the power drives into an oval cross-sectional geometry are not deformed or only a little, - wherein the elastic sleeve in accordance with a control program being executed with the preform extrusion is brought into a substantially cylindrical form when a middle section of the preforms is extruded, and wherein through deformation of the sleeve an oval cross-sectional shape of the sleeve is adjusted when the starting and end sections of the preforms are extruded, which in the blow mould are expanded into the barrel bottom and into the upper barrel termination, - wherein through additional program-controlled actuating movements of the additional element the melt profile of the preforms in the starting and end sections is corrected in order to offset partial thickness differences in circumferential direction in the head and bottom region of the blow-moulded barrels, so that the upper termination of the barrels expanded in the blow mould and the transition region of the barrels between barrel bottom and barrel shell do not have any thickness deviations from preset values in circumferential direction. - wherein the nozzle gap width during the extrusion of the preforms is changed through an actuating movement of the mandrel and/or of the nozzle ring, - wherein the cross-sectional geometry of an elastically deformable sleeve arranged in the nozzle ring or on the mandrel and which delimits the nozzle gap on the circumference side is changed during the extrusion of the preforms either by two power drives located opposite, the actuating movements of which exert pulling forces and/or pressure forces on the sleeve arranged in the nozzle ring in a deformation axis orientated radially to the centre axis of the mandrel, or with a mandrelside arrangement of the sleeve by a vertically orientated power drive which is connected with radially acting actuating elements to the sleeve arranged on the mandrel, - wherein through actuating movements of at least one separately controlled additional element the circumference-side melt distribution in the sections of the preforms, which in the blow mould are expanded into an upper barrel termination and a barrel bottom, is influenced, - wherein the additional element acts on sections of the nozzle gap, which are assigned deformation-neutral regions of the elastically deformable sleeve, which are arranged substantially at 45° to the main deformation axis and during a deformation of the sleeve under the effect of the power drives into an oval cross-sectional geometry are not deformed or only a little, - wherein the elastic sleeve in accordance with a control program being executed with the preform extrusion is brought into a substantially cylindrical form when a middle section of the preforms is extruded, and wherein through deformation of the sleeve an oval cross-sectional shape of the sleeve is adjusted when the starting and end sections of the preforms are extruded, which in the blow mould are expanded into the barrel bottom and into the upper barrel termination, - wherein through additional program-controlled actuating movements of the additional element the melt profile of the preforms in the starting and end sections is corrected in order to offset partial thickness differences in circumferential direction in the head and bottom region of the blow-moulded barrels, so that the upper termination of the barrels expanded in the blow mould and the transition region of the barrels between barrel bottom and barrel shell do not have any thickness deviations from preset values in circumferential direction.