A process for preparing a catalyst which has a catalytically active coating of high surface area finely divided materials and catalytically active components on an inert carrier structure. A powder mixture of the finely divided materials used is impregnated with a solution of precursor compounds of the catalytically active components. By suitable combination of the finely divided materials and the precursor compounds and appropriate management of the impregnation process, a highly dispersed deposition and adsorption of the catalytically active components is ensured on the finely divided materials. Then ai aqueous coating dispersion is produced using the impregnated powder mixture and the carrier structure is coated therewith. The coating is then dried and calcined.