A method for the laser machining of workpieces, in which a laser beam is directed by means of a laser machining head, in which at least one two-dimensionally pivotable scanner mirror connected to an electronic evaluation and control unit is accommodated, onto a workpiece for machining the latter with predeterminable contours and, before the laser machining, a set-actual comparison of the position of the workpiece (4) is carried out with at least one predetermined contour with respect to the laser machining head, wherein a light beam (7) of a light source (1), focused by means of the one or two scanner mirror(s) (2, 3), is directed onto the surface of the workpiece (4) and is deflected along at least one axis by pivoting at least one scanner mirror (2) or (3) and light reflected from the workpiece surface is directed in a focused manner onto an optical detector (5) via the scanner mirror(s) (2, 3);
- the measuring signals of the optical detector (5) are fed to the electronic evaluation and control unit (6) in dependence on the respective pivoting angle of the scanner mirror(s) (2, 3) and
- the deflection of the laser beam (8) is controlled during the machining in dependence on the actual position of the contour (17) ascertained in this way for the machining.