The invention refers to a device for cleaning the teats of an animal, and to a milking stall. The device includes a first conduit member (1) and a teat-cleaning member (2), which is connectable to a central arrangement (3) for supplying cleaning liquid and discharging waste liquid. The teat-cleaning member (2) includes at least two teat-cleaning cups (5) to be applied to a respective teat of the animal, a conduit assembly and two second conduit members (7) extending between a respective one of the teat-cleaning cups and the conduit assembly. Each teat-cleaning cup (5) is connected to the central arrangement (3) via the respective second conduit member (7) and the first conduit member (1) for the supply of cleaning liquid and the discharge of waste liquid.