The kinetics of the oxidation of para-tert-butylcumene to hydroperoxide by molecular oxygen in the presence of N-hydroxyphthalimide has been studied. Based on the study of the regularities in the formation of hydroperoxide and non-target reaction products, a mathematical model of the process was obtained that adequately describes the change in the main components of the reaction concentration over time. The main role of N-hydroxyphthalimide is that it converts peroxide radicals into the corresponding hydroperoxides, thereby reducing the formation of non-target reaction products by reducing the quadratic termination rate. Simultaneously formed N-oxyphthalimide radicals increase the rate of hydrocarbon oxidation. Thus, the use of N-hydroxyphthalimide in hydrocarbon oxidation processes results in an increase in the rate and selectivity of hydroperoxide formation.