A road cutting machine has a machine frame and at least one left-hand running gear and at least one right-hand running gear. A device is provided for raising or lowering the running gears resting on the ground, in relation to the machine frame, and also a control unit is provided for activating the device for raising and lowering the running gears, so that the height of the running gears can be adjusted to the machine frame. The control unit comprises sensors for detecting changes in the height of the ground to be covered by the running gears in relation to the machine frame, whereby the control unit contains a control mode for initiating actions in the control system for adjusting the height of the running gears. The control unit is configured in such a way in the control mode that if a change is detected in the height of the ground, the respective running gear or the respective running gears are raised or lowered so as to compensate any lateral tilting due to a change in the height of the ground.