A steering column module includes a tubular jacket rotatably supporting a steering shaft, a switch module having a carrier including contact pressure surfaces, and a device for fastening the switch module to the tubular jacket. The device includes a clamp assembly between the tubular jacket and the switch module for exerting a clamping force on the tubular jacket. The clamp includes two half clamps each having two outwardly bent end flanges. The end flanges are axially movably accommodated in the carrier such that when the switch module is axially moved onto the tubular jacket the end flanges come into contact with axial end stops of the tubular jacket and the contact pressure surfaces of the carrier. The contact pressure surfaces exert forces on the end flanges as the switch module is axially moved onto the tubular jacket thus fastening the switch module to the tubular jacket with a clamping action.