The catalytic hydrogen-producing processes of two prototypical cobaloxime catalysts, Co(dmgBF(2))(2) (dmgBF(2) = difluoroboryl-dimethylglyoxime) and Co(dmgH)(2) (dmgH dimethylglyoxime), were studied by density functional theory (DFT) and Car-Parrinello molecular dynamics (CPMD) simulations in the explicit acetonitrile-wafer solirent. Our study demonstrates the key role of water molecules as shuttles to deliver protons to the cobalt active centers of these catalysts. However, the transfer of protons to the cobalt centersrfl also competes with the diffusion of the proton away from the complex via the hydrogen bond network of water. Protons were found to react with the oxygen of the side group of Co(dmgH)(2), while a similar reaction was not observed for Co(dmgBF(2))(2). This explains the experimentally observed relative-instability of CO(dmgH)(2) in the acidic medium, The rate-limiting step of the hydrogen-procluchig process was found to be the first proton transfer to the cobalt center for both cobaloxime complexes. Structural and electron population analysis was carried out to provide insight into the origin of the difference of the proton transfer free-energy barriers of these two cobalt complexs. Our study has contributed to the key microscopic understanding of the hydrogen-producing process by this class of catalysts.