A linear friction welding machine comprising a compression unit and an oscillator unit, each having a clamping holder for a workpiece. Both clamping holders are configured such that workpieces are held with the surfaces thereof to be welded, aligned and facing each other. The clamping holder of the compression unit is linearly movable relative to the clamping holder of the oscillator unit, and the latter is movable in an oscillating manner at right angles transversely with respect to the direction of travel of the compression unit and fixed to ends of vertical and horizontal supports which can be deflected laterally in a sprung manner in the oscillation direction, the other ends of which are anchored rigidly on supporting bodies. The supports are flexible under deflection in the oscillation direction but are designed to resist buckling when the clamping holders are loaded in the direction of travel of the compression unit.
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