Abstract: A milking method in which at least one teat cup is connected to a teat of the animal to be milked and milked milk is discharged from the teat cup, and in which upon cessation of the flow of milked milk a cleaning medium is passed via a supply line into the teat cup. Furthermore, the present invention relates to an apparatus which is suited for carrying out the method and comprises at least one teat cup which communicates with a milk line conducting milked milk and in the interior of which a supply line ends via which cleaning medium which has been discharged from a source can be introduced into the teat cup. The present invention provides a method and an apparatus for preventing dirt and germs from penetrating into the milked milk with more reliability. According to the invention the cleaning medium as well as air introduced for discharging the milked milk are introduced via the supply line into the teat cup.