Abstract: A process for preparing 4-substituted 2,2,6,6-tetramethylpiperidin-N-oxy compounds (II) or mixtures of (II) and 4-substituted 2,2,6,6-tetramethylpiperidin-N-hydroxy compounds (III) where X+Y can be O or can represent a cyclic ketal with the radicals or can represent an open-chain ketal in which X?O—R and Y?O—R?, where R and R? can be identical or different and can each be CH3, CH2—CH3, CH2—CH2—CH3, CH(CH3)—CH3, CH2—CH2—CH2—CH3 and CH2—CH(CH3)—CH3, by oxidizing corresponding 4-substituted 2,2,6,6-tetramethylpiperidines (I) with hydrogen peroxide in the presence of alkali metal hydrogencarbonate and/or ammonium hydrogencarbonate and in the presence or absence of a solvent, in which the reaction is carried out with the addition of Brönsted acids which have an acid strength greater than that of the hydrogencarbonate.