Method for cleaning and/or disinfecting a milk-carrying system of a coffee machine for producing coffee mix drinks, wherein the milk-carrying system comprises the following: • a milk preparation device with a milk outlet as well as a fluid inlet, an air inlet and a milk inlet which is designed for conveying milk from the milk inlet to the milk outlet by utilising the Venturi effect; and • a milk delivery line which at one end is connected to the milk inlet and which at another end can be optionally connected to a milk container in such a way that a fluidic connection is established between the milk inlet and the milk container through the milk delivery line, wherein the method comprises the following preparatory process steps: • detaching the milk delivery line from the milk container and connecting the milk delivery line to a first container, which contains an active cleaning and/or disinfecting substance, in such a way that for the active cleaning and/or disinfecting substance a fluidic connection is established between the milk inlet and the first container; and • positioning a second container underneath the milk outlet, and wherein the method comprises the following further process steps in this sequence: i) delivery of fluid, preferably steam, to the fluid inlet in order to convey the active cleaning and/or disinfecting substance through the milk delivery line and the milk outlet into the second container in order to thereby clean and/or disinfect the milk-carrying system; and j) delivery of water to the air inlet and closing of the fluid inlet in order to convey water through the milk delivery line into the first container and to convey water through the milk outlet into the second container, in order to thereby flush the milk-carrying system. • a milk preparation device with a milk outlet as well as a fluid inlet, an air inlet and a milk inlet which is designed for conveying milk from the milk inlet to the milk outlet by utilising the Venturi effect; and • a milk delivery line which at one end is connected to the milk inlet and which at another end can be optionally connected to a milk container in such a way that a fluidic connection is established between the milk inlet and the milk container through the milk delivery line, • detaching the milk delivery line from the milk container and connecting the milk delivery line to a first container, which contains an active cleaning and/or disinfecting substance, in such a way that for the active cleaning and/or disinfecting substance a fluidic connection is established between the milk inlet and the first container; and • positioning a second container underneath the milk outlet, i) delivery of fluid, preferably steam, to the fluid inlet in order to convey the active cleaning and/or disinfecting substance through the milk delivery line and the milk outlet into the second container in order to thereby clean and/or disinfect the milk-carrying system; and j) delivery of water to the air inlet and closing of the fluid inlet in order to convey water through the milk delivery line into the first container and to convey water through the milk outlet into the second container, in order to thereby flush the milk-carrying system.