The invention relates to a device (1) for milking dairy animals, comprising: - a rotatable milking carousel (2) with several milking stations (3), in which each milking station has one or more milk cups (6), - a main milking system for milking a dairy animal with the one or more milk cups comprising a milk pipe system (7) which connects the one or more milk cups with a milk tank (8, 9), characterized in that the device comprises a separation milk system (15) for separating milk from one or more dairy animals, in which a displaceable part (16) of the separation milk system is designed to be displaceable in such a way that the displaceable part can be displaced with respect to the milking carousel in order to be able to cooperate with several milking stations and to move along with a milking station while cooperating with one of the several milking stations, in which the displaceable part of the separation milk system comprises one or more separation milk cups (18), which can be attached to one or more teats of a dairy animal (51) which is situated in or at the milking station, and in which the separation milk system has a separate separation milk pipe system (19) which connects the one or more separation milk cups to a separation milk tank (20), and in which the device has a control device (14) for automatically controlling the displacement of the displaceable part.