A method for producing aryl alkyl hydroperoxides which comprises selectively oxidizing an aryl alkyl hydrocarbon having the formula: ##STR1## wherein P and Q are hydrogen or an alkyl and may be the same or different from each other; x is an integer of 1-3; and Ar is an aromatic hydrocarbon group having a valence of x, with an oxygen-containing gas in the presence of a transition metal complex which contains, as a ligand, a cyclic polyfunctional amine compound having at least three nitrogen atoms in the ring forming molecular chain or an open chain polyfunctional amine compound having at least three nitrogen atoms in the main chain of the molecule.