u03b1 u03b1 u2032 for cutting the workpiece under an oblique cutting angle u03b1 thus the second structural unit 9 b is rotated to a lesser degree as compared to the case when the redirecting mirror 12 is in its rest position by the two coaxial axes b and b u2032 being force connected in technical control terms the control of the macro movement of the laser processing head 9 and the variation of the oblique cutting angle u03b1 can be carried out as if the laser processing beam 2 were orientated coaxially relative to the nozzle axis 3 a alternatively or in addition to the possibility of rotating the redirecting mirror 12 about the b u2032 axis the redirecting mirror 12 can also be rotated about an axis csp which is coaxial relative to the nozzle axis 3 a for which purpose another numerically controlled drive 15 u2032 can be provided in the second structural unit 9 b of the laser processing head 9 as illustrated in fig1 a in any case numerical control of the position of the laser beam 2 on the workpiece 1 can be carried out by providing an additional axis of rotation which extends parallel with the incidence direction of the laser beam 2 on the redirecting mirror 12 b u2032 axis or parallel with the reflection direction of the laser beam 2 csp axis even in the case of eccentric orientation of the laser cutting beam 2 at the cutting gas nozzle 3 in the control unit 16.