Abstract: A method and apparatus for deburring the inner edge of the bore of a workpiece. A tool is introduced into the bore, is rotated at high speed, and has a wobbling movement imparted thereto. Alternatively, the tool can be rotated while a wobbling movement is imparted to the workpiece. The tool is embodied as a grinding rod which is held by a grinder unit which is drivingly connected with an eccentric drive. The grinder unit is preferably pivotable in all directions. During operation, the tool or the workpiece describes, in the bore of the workpiece, a wobbling movement having a circular path which is concentric to the axis of the bore, and having a diameter which increases in the direction toward the free end of the bore. The burr which is to be worked is thus very precisely removed in a simple manner without the danger that the burr is moved into the bore. Furthermore, the tool is embodied in a simple manner, so that it has a long service life.