In the oxidation of cumene to cumene hydroperoxide by molecular oxygen in the liquid phase, the cobalt(II) catalysts heterogenized on organic cation exchangers are active only if acid functional groups of the exchanger which bind cobalt ions show medium or weak acidity. The catalysts based on strongly acidic ion exchangers are inactive and, contrary to the above catalysts, they catalyze decomposition of the cumene hydroperoxide present in the reaction mixture to phenol and acetone.