A driving system is operatable at least in a first automated driving mode with automated longitudinal and/or lateral control, and in a different second automated driving mode with automated longitudinal and/or lateral control. The driving system has a steering wheel display with luminous elements for illuminating the steering wheel, which can be operated in different illumination states that are distinguishable by the driver. The luminous elements may illuminate the steering wheel rim, and are typically integrated into the steering wheel rim. The driving system specifies which illumination state of the different illumination states the steering wheel display has. The driving system specifies that, during operation of the driving system in the first driving mode, the steering wheel display is illuminated in a first illumination state. During operation of the driving system in the second driving mode, the steering wheel display is illuminated in a second illumination state that can be distinguished from the first illumination state by the driver.