A milking system for milking dairy animals includes a milking device, a milk line for transporting milk; a cleaning device for cleaning the milk line with a cleaning liquid; a first outlet for discharging the milk to a milk tank; a second outlet for discharging the cleaning liquid; a valve mechanism for controllably connecting the milk line to one of the first outlet and the second outlet; and a control unit for controlling the valve mechanism. The valve mechanism includes a first and a second valve, and a displacement device for displacing the first or the second valve housing between a cleaning position and a milking position.