The present invention relates to a process for oxidizing hydrocarbons, in particular branched or unbranched saturated aliphatic hydrocarbons, cycloaliphatic or alkylaromatic hydrocarbons to acidic or polyacidic compounds. The invention relates more particularly to the oxidation, with an oxidizing agent containing molecular oxygen, of cyclohexane to adipic acid, in the presence of organic acid of lipophilic nature and in the absence of adipic acid. The separation and recycling of the unoxidized cyclohexane, the oxidation intermediates and the catalysts are easier than in the presence of acetic acid.