The present invention relates to a process for preparing at least one cyclohexanepolycarboxylic acid or a derivative thereof by bringing at least one corresponding benzenepolycarboxylic acid or a derivative thereof into contact with a hydrogen-comprising gas in the presence of at least one coated catalyst comprising an active metal selected from the group consisting of ruthenium, rhodium, palladium, platinum and mixes thereof, applied to a support material comprising silicon dioxide, where the pore volume of the support material is from 0.6 to 1.0 ml/g, determined by Hg porosimetry, the BET surface area is from 280 to 500 m2/g, at least 90% of the pores present have a diameter of from 6 to 12 nm, and from 40 to 70% by weight of the active metal, based on the total amount of the active metal, are present in the catalyst coating up to a penetration depth of 200 μm, wherein the contacting is carried out at a superficial velocity of not more than 50 m/h.