Abstract: A multi-head laser engraving machine with two exposure heads (15, 16) contains a beam splitter (3) belonging to the first exposure head (15), and a tilted mirror belonging to the second exposure head (16). Each exposure head (6, 7) has associated therewith a fast optical switch, the switches being drivable independently of each other by a control unit (9). This permits simultaneous and independent inscription of the working areas (F1, F2) associated with the respective exposure heads (15, 16). The fast optical switches have the form of a deflection prism which is swiveled into the focused partial beam in order to interrupt the beam.