The present invention concerns a process for oxidizing cumene to cumene hydroperoxide using an oxygen containing gas, preferably air, which process comprises —conducting a cumene feed and an oxygen containing gas feed to at least the first oxidation reactor in a series of 3-8 reactors, thereby forming an oxidation mixture, and conducting the formed oxidation mixture from one reactor to the next, preferably after an oxidation reaction has taken place, wherein —the reactors comprise at least one lower pressure oxidizer (1) as the first reactor in the series and at least one higher pressure oxidizer (2) as the last reactor in the series; —any lower pressure oxidizer is operated at a pressure of at least atmospheric pressure and any higher pressure oxidizer is operated at a pressure of at least 0.5 bar higher than said at least one lower pressure oxidizer.