A milking system includes a milking member for extracting milk from an animal, a transport line, a milk tank, a milk filter unit for filtering the milk with a first filter device and a second filter device, each including a filter container and a filter element, and a valve arrangement to convey milk through the devices, where the valve arrangement communicates with a control unit. The milking system further includes an indication device generating an indication to a user when any one of the filter elements needs to be replaced, which filter of the first and second filter device needs to be replaced, and when the filter element indicated to need to be replaced is accessible for replacement. A method for operating and cleaning the milking system is also provided.