A laser beam apparatus for processing workpieces includes a beam transmission system providing a beam pathway therethrough from the laser beam generator to a laser focusing head, and this system has at least one mirror which reorients the direction of the beam in the pathway and which is adjustable in at least one axis relative to the pathway. At a point downstream of the mirror is a laser beam sensing means which senses deviation of the beam from its optimum path and generates a signal which is transmitted to deviation responsive means to provide an output. This output may include a visual indicator which enables the operator to effect manually the necessary adjustment of the mirror or an automatic operating means for effecting corrective movement of the mirror. The apparatus has a laser cutting head containing a beam directing mirror and the focusing lens with a deviation sensing means therebetween. This is movable along two axes which are perpendicular to each other, it may also be pivotable about one of the axes, and it may also be movable along a third axis perpendicular to the first two axes.