Abstract: A self-propelled substrate milling machine includes a machine frame supported by front and rear left-hand and right-hand running gear units, wherein a milling drum is arranged on the machine frame. The substrate milling machine is characterized by a transverse inclination sensor system, which is designed to control the substrate milling machine in such a way that the position of the front left-hand and right-hand running gear units which stand on the unmachined substrate, is detected with respect to the machine frame, and transverse inclination values describing the transverse inclination of the substrate surface transverse to the working direction of the substrate milling machine with respect to the machine frame is determined from the position of these running gear units, said transverse inclination values being the basis for the control of the substrate milling machine. The transverse inclination sensor system detects the transverse inclination of the course of the route.