PURPOSE: To selectively obtain a arylalkylhydroperoxide compound in a small amount of a catalyst in a high reaction rate and in a high concentration by oxidizing the corresponding arylalkyl hydrocarbon in the presence of a specific transition metal complex as the catalyst.

CONSTITUTION: An arylalkyl hydrocarbon of formula I (P, Q are H, an alkyl; x is 1-3; Ar is a x-valent aromatic hydrocarbon group) (preferably cumene) is oxidized with an oxygen-containing gas in the presence of (B) a transition metal complex comprising (i) a ligand of formula II (M is a transition metal-) [preferably N,N'-bis(1-methyl-3-oxobutylidene)ethylenediamine, etc.,) and (ii) a transition metal ion (preferably Mn, Co, Fe, Cu, Rh, Ru or Cr ion) as a catalyst to obtain the objective corresponding compound. The component B is preferably a compound of formula II (R1-R8 are H, an organic group).