In the production of a mineral product that consists of aluminum layer silicate and corresponding fines with an at least 70% proportion of the mineral illite of the selected type, the starting material in its natural composition is pre-broken, the agglomerated layer silicate particles are subjected to a deagglomeration at a high acceleration rate and swirled using strong air masses, the agglomerates are broken up into primary crystallites by being slammed against one another and against impact surfaces, the deagglomerated layer silicate particles are drawn off by fine sifting and the deagglomerated particles are returned to the cycle, and the deagglomerated primary crystals are drawn off.