Abstract: To excavate drifts, tunnels, stopes, caverns or the like, tools operating in an undercutting manner are mounted on radially pivotable tool arms, which are located on a rotary working head. With at least one tool (54) on a tool arm (51), a central region (Z) of the rock face is cut radially from the outside inwards by pivoting of the tool arm (32), an outer region (A) surrounding the central region (Z) of the rock face is cut radially from the inside outwards by pivoting of the tool arm (32). Pivot drives (30) for at least some tool arms (31, 32, 33) can be controlled in such a manner that cross-sections with contours deviating from a full circular shape can be cut. Muck removing devices (27, 28) are used for collecting and transporting away the muck produced by the cutting operation.