For supplying a pressurized cooling liquid to the outlet openings in a cutting head, there is provided an axial supply bore (3) opening into a distributing chamber. Radial passages (11) are provided which open into the distributing chamber and lead to the outlet openings at the periphery of the rotating cutting head. The distributing chamber is designed as a space coaxially surrounding the axial bore (3), being closed at its front side and having its mantle stationary arranged. At least two radial bores (9, 10) of opposite radial direction adjoin this annular space and are displaced in axial direction of the bore (3). The cutting head is sealingly guided on the non-rotating mantle of the annular space.