Abstract: The invention relates to a method for machining workpieces by using laser radiation, wherein the workpieces to be machined are moved during the machining and at least one laser beam is deflected with respect to two axes aligned orthogonally to one another. It is therefore the object of the invention to form large-area machining contours with as high a machining speed and as great an accuracy as possible. In the method in accordance with the invention, a procedure is followed that a laser beam is deflected within a working field with respect to two axes aligned orthogonally to one another. Positional coordinates of the respective machining contour are moreover associated in an electronic evaluation and control unit with virtual machining segments in which the machining is carried out sequentially.