The invention relates to a crushing or grinding element for drum refiners having an engine-driven rotor for the crushing or grinding of fibrous materials. The element is attachable to the rotor shell and has crushing or grinding surfaces of increasing diameter and optionally crushing or grinding surfaces of steeper inclination to the rotor axis immediately adjacent the crushing or grinding surfaces inclined to the rotor axis provided on the rotor shell. The grinding surfaces are symmetrical to the median plane of the material feed. The invention is characterized in that the crushing or grinding element(s) is (are) formed as (a) segment(s) placed around the circumference of the rotor having anchoring projections of hammerhead-like cross section on the side facing the rotor axis and which are engageable in corresponding rotor grooves of hammerhead-like cross section.