Abstract: A tool for fine machining the tooth flanks of pretoothed gearwheels is described. The flanks of the gearwheel are subjected to a worm-shaped tool by the hobbing method. The tool is made of an elastic synthetic material with embedded granular grinding material. It is advantageous for the worm-shaped tool to be lined up with a conventional grinding worm on a tool spindle. The microfinish of the gearwheel, i.e. the polishing, can then take place on one and the same machine directly following the grinding.