Abstract: A machine for successively grinding and polishing tools such as gravers of hard metal has grinding and polishing wheels mounted in parallel shafts on a support which can be moved to bring either wheel to face a tool held in a workpiece holder. The polishing wheel can be moved to an extreme position which is precisely set by a micrometer screw so that it comes to occupy exactly the same position formerly occupied by the grinding wheel. Alternatively, the workpiece-carrier can be moved by a cam system to exactly position the tool against the two wheels.