Movable elements of a machine are moved by a control device of the machine by controlling drives of the machine. To monitor the movement of the movable elements for collision with each other or with a stationary element, two monitoring devices check, independently from each other, using a computer program, whether there is a risk of collision in the working space. Depending on whether the monitoring devices detect a risk of collision or not, they intervene, independently from each other, in a corrective manner, in the control of the drives or not, and/or independently emit an alarm message or not. The two computer programs are designed in a diverse manner. The two monitoring devices differ from one another. One monitoring device is identical to the control device, while the other monitoring device is embodied as an industrial PC with a data link to the control device.