The kinetics and mechanisms for N2H4+NOx (x=1-3) reactions and the related reverse reactions have been investigated by ab initio molecular orbital theory based on the CCSD(T)/CBS//CCSD/6-31G(d,p), CCSD(T)//B3LYP and CCSD(T)//BH&HLYP methods with the 6-311++G(3df,2p) basis set. These reactions are important to the propulsion chemistry of the N2H4-N2O4 propellant system. The results show that the reactions of N2H4 with NO and NO2 producing N2H3+HNO and N2H3+c-HONO by H-abstraction with 33.7 and 10.3kcal/mol barriers, respectively, are dominant. For the N2H4+NO3(D3h) reaction via two pre-reaction van der Waals complexes with 0.5kcal/mol and -1.6kcal/mol binding energies produces HNO3+N2H3 by H-abstraction and t-HONO+N2H3O by concerted O- and H-atom transfers, respectively. The predicted enthalpies of formation of various products at 0K are in good agreement with available experimental data within reported errors. Furthermore, the rate constants for the forward and some key reverse reactions have been predicted in the temperature range 300-2000K with tunneling corrections using transition state theory (for direct abstraction) and variational Rice-Ramsperger-Kassel-Marcus theory (for association/decomposition) by solving the master equation.