By means of the laser-beam welding process using two beams guided in succession, it is possible to achieve a substantial reduction in the hardness increase in the weld and in the heat-affected zone. A conventional installation for laser-beam welding was therefore converted in such a way that the laser beam could be divided into a main beam and an auxiliary beam. Furthermore, it was possible to alter the distance between the focal points by shifting the auxiliary beam in relation to the main beam. Welding experiments on the 25CrMo4 and S355J2G3 steels indicated that the maximum hardness of the weld can be influenced distinctly not only by the percentage division of the laser-beam power but also by the distance between the two focal points.