Abstract: An apparatus to process, in particular, curved surfaces using one or more grinding or polishing tools which includes a housing (2) having a drive system (3, 20, 19, 12) powering at least one tool seat (1) particularly for a grinding or polishing tool (W) into rotation about a longitudinal axis (4). For the purpose of multi-sided pivoting displacement of the axis of rotation (4) within a predetermined angular range (&agr;), the tool seat (1) rests pivotably in a holder (5) of the housing (2), the holder (5) including a shell (7) having an outer contour in the shape of a spherical segment and being pivotably received in an inner contour of a seat (8) also in the shape of a spherical segment. The drive system (3, 20, 19, 12) includes a pivoting ball-joint (6) coupling it to the tool seat (1) in order to drive the seat into rotation in every pivoted position.