Abstract: The invention relates to a cutter head having a substantially cylindrical main body and a plurality of replaceably cutting elements disposed at the periphery of said main body and having at least one cutting edge in the axial and/or radial direction of said main body. For achieving a reliable three-dimensional adjustment of the cutting members within extremely close tolerances, each cutting member is mounted on a carrier member itself mounted on said main body and adapted to be radially and axially adjusted relative to the main body by means of separate adjustment means disposed between said main body and said carrier member, and to be fixed relative to said main body with the aid of clamping means.