Cleaning system for cleaning the cooking chamber of a cooking appliance having a ventilation device, comprising - a supply system, comprising ∘ at least a first supply device for water, the device having a reservoir for water and, arranged in the direction of flow of the water, an element for increasing the pressure and a water check valve, ∘ at least a second supply device for cleaning agent, the device having a reservoir for cleaning agent and, arranged in the direction of flow of the cleaning agent, a cleaning agent conveying unit and a cleaning agent check valve, - a circulation circuit which comprises, as components, ∘ at least one connection device which is in contact with a first opening of the cooking chamber and is designed as an outlet or inlet, ∘ at least one return pipe which is in contact with a second opening of the cooking chamber and is arranged along the vertical above the connection device, ∘ at least one circulation device, ∘ at least one shut-off member which is designed in such a way that it fluidically connects the connection device and the return pipe to one another or separates them from one another, wherein in the event of a fluidic separation, the shut-off member is designed in such a way that it fluidically connects the connection device to a drain, ∘ at least one distribution device which is designed as a mixing and metering device, - at least one control device having a computer program product, which device is connected to the shut-off member using information technology, wherein the components of the circulation circuit are fluidically connected to one another by means of connection elements (17, 18, 19, 20), and wherein the first and second supply devices of the supply system open in the distribution device in the direction of flow. - a supply system, comprising ∘ at least a first supply device for water, the device having a reservoir for water and, arranged in the direction of flow of the water, an element for increasing the pressure and a water check valve, ∘ at least a second supply device for cleaning agent, the device having a reservoir for cleaning agent and, arranged in the direction of flow of the cleaning agent, a cleaning agent conveying unit and a cleaning agent check valve, ∘ at least a first supply device for water, the device having a reservoir for water and, arranged in the direction of flow of the water, an element for increasing the pressure and a water check valve, ∘ at least a second supply device for cleaning agent, the device having a reservoir for cleaning agent and, arranged in the direction of flow of the cleaning agent, a cleaning agent conveying unit and a cleaning agent check valve, - a circulation circuit which comprises, as components, ∘ at least one connection device which is in contact with a first opening of the cooking chamber and is designed as an outlet or inlet, ∘ at least one return pipe which is in contact with a second opening of the cooking chamber and is arranged along the vertical above the connection device, ∘ at least one circulation device, ∘ at least one shut-off member which is designed in such a way that it fluidically connects the connection device and the return pipe to one another or separates them from one another, wherein in the event of a fluidic separation, the shut-off member is designed in such a way that it fluidically connects the connection device to a drain, ∘ at least one distribution device which is designed as a mixing and metering device, ∘ at least one connection device which is in contact with a first opening of the cooking chamber and is designed as an outlet or inlet, ∘ at least one return pipe which is in contact with a second opening of the cooking chamber and is arranged along the vertical above the connection device, ∘ at least one circulation device, ∘ at least one shut-off member which is designed in such a way that it fluidically connects the connection device and the return pipe to one another or separates them from one another, wherein in the event of a fluidic separation, the shut-off member is designed in such a way that it fluidically connects the connection device to a drain, ∘ at least one distribution device which is designed as a mixing and metering device, - at least one control device having a computer program product, which device is connected to the shut-off member using information technology,