Aggregate abrasive grains for use in the production of abrading or cutting tools are formed such that each grain includes an abrasive core particle and a plurality of abrasive peripheral particles disposed around the core particle. The abrasive particles intended as the core particles are provided with a coating containing a binder. These binder-coated core particles are then surrounded with those particles that are intended to become the peripheral particles of the aggregate grains. The binder-coated core particles surrounded with the peripheral particles are heated to a temperature at which the binder softens so that the peripheral particles attach to the core particles.