Milk supply device for supplying milk (M) from a milk supply container (1) to a milk dispensing device (4), comprising a milk transport line (20) which can be connected or is connected at a first (7) of the ends (7, 21) thereof to the milk supply container (1) and with which, via a second (21) of the ends (7, 21) thereof, milk (M) which has been taken from the milk supply container (1) can be delivered to the milk dispensing device (4), characterised in that by means of a cleaning agent transport line (12) which is in fluid communication with the milk transport line (20) between the first end (7) and the second end (21),a three-way junction (6, 6', 6") is configured which can be operated such that optionally ‧either in a milk flow operating state (MFBZ), milk (M) can be transported via it (6, 6', 6") from the milk supply container (1) to the milk dispensing device (4), whilst the milk transport line (20) is sealed off by it (6, 6', 6"), at the same time, relative to the cleaning agent transport line (12), in a fluid-impermeable manner, ‧or in one or more cleaning operation state/states (RBZ1, RBZ2, RBZ3), cleaning agent (R) can be conducted from the cleaning agent transport line (12) which is in fluid communication with it (6, 6', 6"), via it (6, 6', 6") in the direction towards the milk dispensing device (4) and/or in the direction towards a discharge (11) of the milk supply device.一種牛奶供應裝置,用於從一牛奶供應容器(1)供應牛奶(M)至一牛奶分配裝置(4),其包括:一牛奶傳輸線(20),其於其端部(7,21)之一第一端(7)可被連接或被連接至該牛奶供應容器(1),且經由其端部(7,21)之一第二端(21),將從該牛奶供應容器(1)取得之牛奶(M)傳送至該牛奶分配裝置(4),其特徵為藉由在該第一端(7)以及該第二端(21)之間與牛奶傳輸線(20)以流體連通之一清潔劑傳輸線(12),一三通接頭(6、6'、6")被設置以進行選擇操作:‧在一牛奶流操作態(MFBZ)中,牛奶(M)經由三通接頭(6、6'、6")從該牛奶供應容器(1)傳輸至該牛奶分配裝置(4),同時該牛奶傳輸線(20)被該三通接頭(6、6'、6")封住,同時相對於該清潔劑傳輸線(12),係使用一液體不滲透之方式, ‧或在一或多個清潔操作態(RBZ1、RBZ2、RBZ3)中,清潔劑(R)是從該清潔劑傳輸線(12)被導引,該清潔劑傳輸線與該三通接頭(6、6'、6")係以流體連通,經由該三通接頭(6、6'、6")朝向該牛奶分配裝置(4)之方向及/或朝向該牛奶供應裝置之一排出裝置(11)之方向。