The reactions between ground-state oxygen atoms (O((3)P)) and the ammonia (NH(3)) and hydrazine (N(2)H(4)) molecules have been studied using electronic-structure and dynamics calculations. Ab initio calculations have been used to characterize the primary reaction channels accessible at hyperthermal energies. These reaction channels are i) hydrogen abstraction, O + NH(3)(N(2)H(4)) --> OH + NH(2)(N(2)H(3)), ii) H-elimination O + NH(3)(N(2)H(4)) --> H + ONH(2)(ON(2)H(3)), and iii) N-N breakage (in the reaction involving hydrazine), O + N(2)H(4) --> ONH(2) + NH(2). Hydrogen abstraction is the lowest-barrier process, followed by N-N breakage and H-elimination. Comparison of our highest-accuracy calculations (CCSD(T)/CBS//MP2/aug-cc-pVDZ) with a variety of lower-cost electronic-structure methods shows that the BHandHLYP method, in combination with the 6-31G* basis set, captures remarkably well the essential features of the potential-energy surface of all of the reaction channels investigated in this work. Using directly the BHandHLYP/6-31G* combination, we have propagated quasiclassical trajectories to characterize the dynamics of the O + NH(3) and O + N(2)H(4) reactions at hyperthermal energies. The trajectory calculations reveal that hydrogen abstraction is the dominant reaction channel, with cross sections between a factor of 2 and an order of magnitude larger than those for the H-elimination and N-N breakage channels. The dynamics calculations also indicate that most of the energy is partitioned into products relative translation but significant vibrational excitation of products is possible as well. Analysis of angular distributions and opacity functions suggests that whereas the hydrogen-abstraction reactions proceed through a mechanism with a substantial component of stripping dynamics, H-elimination and N-N breakage are dominated by rebound dynamics.