This work employed the quantum-chemical method at the CCSD(T)/6-311+G(3df,2p)//B3LYP/6-311+G(3df,2p) level to study the mechanisms and kinetics of N2O4 (NTO) with H2NN(CH3)(2) and CH3NHNHCH3 hypergolic initiation reactions, the processes critical to the chemical rocket propulsion of the N2O4-hydrazine propellant systems. The reaction of N2O4 with the dimethylhydrazines (DMHZ's) can be started by the fast reaction of DMHZ's with ONONO2, taking place after the novel N2O4 -> ONONO2 transformation with each of DMHZ's as a spectator within the NTO-DMHZ collision complexes, through loose, roaming-like transition states during the bimolecular encounters. The barriers for such isomerization processes were found to be 7.2 and 9.9 kcal/mol for H2NN(CH3)(2) and CH3NHNHCH3, respectively. The kinetics of these reactions have been computed in the temperature range 200-2000 K; the results indicate that under the ambient temperature and pressure condition, the half-life of NTO in the presence of an excess amount of H2NN(CH3)(2) is predicted to be 3.3x10(-5) s. The results of a similar estimate for CH3NHNHCH3 is about 2 orders of magnitude longer; both estimates indicate that very effective hypergolic reactions can occur upon mixing in these systems.