To gain access to the cutting edge (53) of a saw tooth (5) in the direction of both the back and the front face of a tooth in a single grinding process, the grinding tools (27,37) are adjustable in relation to both their respective pivoted arms (2,3) and with them relative to the machine frame (11,12). Only the primary pivoted arm (2) is driven up and down by a drive (43), pivoting the secondary arm (3) with it by a drive joint (6). Because the pivot axes of pivoted arms (2,3) are not parallel, a universal coupling (6) must be used. This drive joint (6) is offset relative to the pivot axles (32) upwardly from the saw-blade guide (13) in the plane (14) of the saw-blade. Thereby with an otherwise identical device wide or larger-diameter saw blades can be ground.