A device for securing a slitter or scorer head to a rotary shaft. The head is slidably mounted on the rotary shaft and a constriction means is provided between the head and shaft. The constriction means comprises a constriction element provided on the inner periphery of the head, and a flat support face provided on the outer periphery of the shaft along the longitudinal axis thereof. The constriction element is projected from the inner periphery of the head into an aperture formed by the flat support face and the inner periphery of the head. The aperture has a section like a segment of a circle and is adapted to be higher than the projection. The slight rotation of the head in respect to the shaft causes the constriction element to pressure-contact with or separate from the flat face of the rotary shaft, the head thereby being fixed or released from fixing.