The Zr-monosubstituted Keggin-type dimeric phosphotungstate (Bu4N)8[{PW11O39Zr(μ-OH)(H2O)}2] (1) efficiently catalyzes epoxidation of C═C bonds in various kinds of alkenes, including terminal ones, with aqueous H2O2 as oxidant. Less sterically hindered double bonds are preferably epoxidized despite their lower nucleophilicity. Basic additives (Bu4NOH) in the amount of 1 equiv per dimer 1 suppress H2O2 unproductive decomposition, increase substrate conversion, improve yield of heterolytic oxidation products and oxidant utilization efficiency, and also affect regioselectivity of epoxidation, enhancing oxygen transfer to sterically hindered electron-rich C═C bonds. Acid additives produce a reverse effect on the substrate conversion and H2O2 efficiency. The reaction mechanism was explored using a range of test substrates, kinetic, and spectroscopic tools. The opposite effects of acid and base additives on alkene epoxidation and H2O2 degradation have been rationalized in terms of their impact on hydrolysis of 1 to form monomeric species, [PW11O39Zr(OH)(H2O)x]4- (1-M, x = 1 or 2), which favors H2O2 homolytic decomposition. The interaction of 1 with H2O2 has been investigated by HR-ESI-MS, ATR-FT-IR, and 31P NMR spectroscopic techniques. The combination of spectroscopic studies and kinetic modeling implicated the existence of two types of dimeric peroxo complexes, [Zr2(μ-η2:η2-O2){PW11O39}2(H2O)x]]8- and [{Zr(μ-η2-O2)}2(PW11O39)2(H2O)y]10-, along with monomeric Zr (hydro)peroxo species that begin to dominate at a high excess of H2O2. Both dimeric μ-η2-peroxo intermediates are inert toward alkenes under stoichiometric conditions. V-shape Hammett plots obtained for epoxidation of p-substituted styrenes suggested a biphilic nature of the active oxidizing species, which are monomeric Zr-hydroperoxo and peroxo species. Small basic additives increase the electrophilicity of the catalyst and decrease its nucleophilicity. HR-ESI-MS has identified a dimeric, most likely, bridging hydroperoxo species [{PW11O39Zr}2(μ-O)(μ-OOH)]9-, which may account for the improved epoxidation selectivity and regioselectivity toward sterically hindered C═C bonds.