Primary hydroxyl groups in a substrate having both primary and secondary hydroxyl groups can be selectively oxidized to carbaldehyde and/or carboxyl groups by contacting the substrate with a cyclic nitroxyl compound in the presence of a peroxosulfate as a co-oxidant and by carrying out the reaction at a temperature below 30 C. and at a pH below 9. The process is halogen-free and metal-free and is especially suitable for oxidizing polysaccharides.