Method for processing of tubes by cutting in a laser tube cutting machine and laser tube cutting machine

A laser tube cutting machine for processing of tubes by cutting, the laser tube cutting machine comprising:

• a push-through device having clamping jaws;
• a workpiece moving device receiving a tube and moving the tube in an X-direction relative to said push-through device, said push-through device supporting the tube when guided in Y and Z-directions by said clamping jaws of said push-through device;
• a laser machining device associated with said push-through device and having a processing head directing a laser beam emerging from said processing head onto the tube;
• a processing device having at least one tool for mechanical processing of the tube, said at least one tool being moveable in at least one direction of movement relative to the tube;
• and
• at least one counterholder being moveable into a working position for abuting against the tube, said counterholder acting in an opposite direction to a direction of application of force of said at least one tool.