A milking system includes several milking devices, each having a milk-carrying part, a temporary milk storage vessel, a milk pipe system, a milk storage tank, and a main milk pipe, which connects the temporary milk storage vessel to the milk storage tank. The milking system includes a first cleaning device having at least one first cleaning liquid supply and at least a pump, which cleaning device is configured to clean at least the milk-carrying part of at least one milking device and a part of the milk pipe system which connects the milk-carrying part to the temporary milk storage vessel, by transferring cleaning liquid from the cleaning liquid supply through at least the milk-carrying part of the at least one milking device and through said part of the milk pipe system to the temporary milk storage vessel by pumping. The temporary milk storage vessel includes a main pump for transferring liquid from the temporary milk storage vessel through the main milk pipe in the direction of the milk storage tank. The milking system includes a second, additional cleaning device with at least one second, additional cleaning liquid supply, which second cleaning device is configured to supply additional cleaning liquid from the second cleaning liquid supply in a direction of flow from the temporary milk storage vessel towards the main milk pipe. The second cleaning liquid supply is situated downstream of at least each of the milking devices, viewed in said direction of flow.
