Pentasil coated catalysts and fully crystalline catalysts in which the individual pentasil crystals are larger than 5 .mu.m are prepared by hydrothermal treatment of SiO.sub.2 by a process in which the SiO.sub.2 moldings are subjected to a hydrothermal treatment at from 140.degree. to 220.degree. C. in an alkali-free mixture of water, an amine and/or a tetraalkylammonium compound, with or without ammonia. The aluminum component for the preparation of an aluminosilicate zeolite can be kneaded into the SiO.sub.2 moldings or fed in via the liquid phase during the hydrothermal treatment. The tetraalkylammonium compound used can be a tetra-n-propyl-ammonium salt or hydroxide.