An impact crusher wherein hard particulate material is comminuted during travel between a rotor provided with beaters and a pivotable impact or grinding means, the latter being mounted in the housing of the crusher at a level above the rotor and tends to pivot by gravity and/or by spring force in a direction to reduce the width of the gap between its lower portion and the periphery of the circle swept by the rotor beaters. The impact or grinding means is pivotable by feed screws which are articulately connected thereto and extend upwardly through openings in the top wall of the housing. The outer portions of the feed screws are rigid with a crosshead which can be moved up and down by a double-acting hydraulic cylinder and piston unit which has an appropriate lost motion to allow the impact or grinding means to yield in direction away from the rotor. When the cylinder and piston unit lifts the crosshead, additional cylinder and piston units can readily shift stepped or wedge-like inserts which are movable between the crosshead and the top wall of the housing to thereby determine the minimum width of the gap. The inserts can be engaged directly by the underside of the crosshead or by a platform which can be mounted beneath the crosshead. When the adjusting mechanism for the impact or grinding means employs a platform, packages of dished springs are inserted between the platform and the crosshead.