The catalytic effects of small amounts of H2O (similar to 10(-3) mol/l), introduced in the ethylbenzene oxidation with molecular O-2 catalysed with {Fe(III)(acac)(3) + R4NBr} systems, where R4NBr = exo ligands-modifiers, quaternary ammonium salts CTAB, (C2H5)(4)NBr, Me4NBr, were discovered by us. The synergetic effects of increase in the selectivity (S-PEH) and the conversion degree (C) (parameter (S) over tilde .C) of ethylbenzene oxidation with molecular O-2 to a-phenylethylhydroperoxide (PEH) were obtained in the case of ethylbenzene oxidation catalysed with {Fe(III)(acac)(3) + CTAB+ H2O} system. The proposed 'dioxygenase-like' mechanism of iron catalyst transformation into new catalytic particles in the course of oxidation process in the presence {Fe(III)(acac)(3)(+) R4NBr} and activating additives of the water is discussed. The method of evaluation of the activity of formed complexes (Fe(II)(acac)(2))(x)(R4NBr)(y)(H2O)(n) in the micro-stages of the catalytic chain-radical ethylbenzene oxidations is offered.