Abstract: The apparatus comprises a saw blade holder (24), a grinding slide (30) which carries a profiled grinding wheel (38) and is movable to and fro in a strokewise manner with respect to the saw blade holder (24), and a feed slide (40) by means of which a saw blade (10) in the saw blade holder (24) can be advanced in a stepwise manner. A dressing template (50) is arranged at the apparatus in a normally inoperative position and can be moved in intervals into an operative position in which the grinding wheel (38) is dressed by plunging into the dressing template (50). The feed slide (40) can be put out of operation during the dressing intervals. The stroke of the grinding slide (30) is adjustable prior to the next plunging motion into the saw blade (10) corresponding to the radius decrease of the grinding wheel (38) effected by dressing. This simplifies the dressing operation of the grinding wheel (38) and shortens the time required for each dressing operation.