Abstract: The present invention relates to an arrangement for grinding planar annular surfaces (6; 8), especially the sealing surfaces of a valve. The arrangement comprises a hub (15) disposed rotationally fixed and bearing a planetary disc (16) mounted rotatably on the hub (15) and bearing in turn around its periphery a plurality of grinding heads (17) each having a grinding disc (19) mounted rotatably in its respective grinding head (17). The planetary disc (16) is effectively connected to a drive shaft (4) by means of which it can be caused to rotate relative to the hub (15). Between the hub (15) and the grinding discs (19) there are effective connections (31, 32, 33, 34, 35, 36) adapted to cause the grinding discs (19) to rotate relative to their respective ginding heads (17) when the planetary disc (16) is rotated relative to the hub (15). It is characteristic of the invention that the drive shaft (4) is mounted in the center of the hub ( 15) in such a way that it can be pivoted through approximately 180.degree.