In an automotive milling machine, with a machine frame with longitudinal axis, with a chassis with wheels or tracked travelling drive units which support the machine frame, with a controller for the travelling, steering and milling operation, with a height-adjustable working drum, with a slewable last or single transport conveyor of specified length arranged in front of or behind the working drum as seen in the direction of travel of the milling machine, where the transport conveyor is, as a minimum, slewable sideways about an essentially vertical first axis under a slewing angle, it is provided for the following features to be achieved: the controller comprises a detection and control system which, as a minimum, detects the steering angle of the steering controller for the chassis or, as a minimum, the steering angle of the steering controller and the distance travelled or the travel speed, and controls the slewing angle of the transport conveyor in accordance with this no less than one parameter.