The kinetics of the liquid-phase oxidation of alkylarenes with molecular oxygen in the presence of the initiators azobisisobutyronitrile and benzoyl peroxide and the catalyst N-hydroxyphthalimide (NHPI) was studied. It was found that the rate of oxidation of alkylarenes depended on the partial pressure of oxygen, an effect that is explained by its involvement in the reaction with NHPI resulting in the initiation of the oxidation chain.