An apparatus for the milling cutting of rock, minerals or other hard materials has a tool drum which is rotatably mounted on a drum carrier about a drum axis and on the peripheral shell surface of which are disposed, in distributed arrangement, a plurality of tool carriers, which carry cutting tools and can be rotatingly driven, where their shaft axes run transversely to the drum axis. A first group of tool carriers and a second group of tool carriers are provided, where the rotational direction of the first group is counter to the rotational direction of the second group, and the shaft axes of the tool carriers of the first group and of the second group are oriented at different setting angles relative to the radial direction of the tool drum.