Pressing system for a laser joining system for pressing a base plate and a storage cell together in the region of a joining point (5, 5a, 5b) in order to produce a power storage means, comprising - a receptacle for accomodating the base plate and the storage cell, - a pressing element (7, 7') for locally pressing the base plate and the storage cell together in the region of the joining point (5, 5a, 5b), - a positioning system for the relative positioning of the pressing element (7, 7') and the receptacle and for pressing the base plate and the storage cell together during the joining process, having • a parallel positioning device (8, 8') for the relative positioning of the receptacle and the pressing element (7, 7') in parallel with a plane and • an oblique positioning device (9, 9') for the relative positioning of the pressing element (7, 7') and the receptacle obliquely, in particular transversely, to the plane and for pressing the base plate and the storage cell together during the joining process, - the pressing system having at least two pressing elements (7, 7') and at least two oblique positioning devices (9, 9'), characterized in that the pressing system has at least two parallel positioning devices (8, 8') and the pressing system is configured to press the base plate and the storage cell together at a first joining point (5, 5a, 5b) using a first pressing element (7, 7'), while a second pressing element (7, 7') is displaced to a second joining point (5, 5a, 5b) so that parts to be joined can then be pressed together and joined there. - a receptacle for accomodating the base plate and the storage cell, - a pressing element (7, 7') for locally pressing the base plate and the storage cell together in the region of the joining point (5, 5a, 5b), - a positioning system for the relative positioning of the pressing element (7, 7') and the receptacle and for pressing the base plate and the storage cell together during the joining process, having • a parallel positioning device (8, 8') for the relative positioning of the receptacle and the pressing element (7, 7') in parallel with a plane and • an oblique positioning device (9, 9') for the relative positioning of the pressing element (7, 7') and the receptacle obliquely, in particular transversely, to the plane and for pressing the base plate and the storage cell together during the joining process, • a parallel positioning device (8, 8') for the relative positioning of the receptacle and the pressing element (7, 7') in parallel with a plane and • an oblique positioning device (9, 9') for the relative positioning of the pressing element (7, 7') and the receptacle obliquely, in particular transversely, to the plane and for pressing the base plate and the storage cell together during the joining process, - the pressing system having at least two pressing elements (7, 7') and at least two oblique positioning devices (9, 9'), characterized in that the pressing system has at least two parallel positioning devices (8, 8') and the pressing system is configured to press the base plate and the storage cell together at a first joining point (5, 5a, 5b) using a first pressing element (7, 7'), while a second pressing element (7, 7') is displaced to a second joining point (5, 5a, 5b) so that parts to be joined can then be pressed together and joined there.