During welding with high output power, the gaps between the pieces being joined may not exceed a maximal gap width. A process for laser beam welding is provided, which on the one hand ensures maintaining (not exceeding) a maximal gap width between the sheets and on the other hand makes possible a maximal utilization of the achievable welding speed. The sheets, prior to welding, are first spot welded, wherein they are clamped only during this spot welding in order to ensure the maintenance of a maximum gap width.