The present invention relates to a process for the oxidation of hydrocarbons, in particular of branched or unbranched saturated aliphatic hydrocarbons, of cycloaliphatic or alkylaromatic hydrocarbons or of alcohols and/or ketones, to acid or polyacid compounds.It relates more particularly to the oxidation, by an oxidizing agent comprising molecular oxygen, of cyclohexane and/or of cyclohexanol and/or cyclohexanone to adipic acid, in the presence of an aromatic organic acid and a manganese-based catalyst. The yield and selectivity for adipic acid are of a high level with respect to those obtained with other solvents and catalysts.