Abstract: The invention relates to a method of and apparatus for dry grinding a granular material in a grinding tube mill (1) having a final grinding compartment (2) and one or more preceding grinding compartments (3) containing grinding bodies. The material, after having passed through the preceding compartment or compartments (3), is discharged through openings (6) in the mill (1) and is divided into a fine and a coarse fraction in a separator (9). The coarse fraction is returned to the preceding compartment or compartments (3), and the fine fraction is fed to the final compartment (2). The ground material is discharged by flowing over a dam ring (12) from the final compartment (2). Any grinding bodies carried with the overflow are separated by a sieving diaphragm (13) from the material and returned to the final compartment (2). The invention also relates to the granular material ground according to the method of the invention.