In this review, we consider the reactions of NO ( x 1,2) with the nitrogen x hydrides NH, NH and NH . The reactions are relevant to the post-combustion, non-catalytic reduction of NO with NH in the thermal de-NO process and with x x HNCO in the rapid reduction of NO as well as to the thermal decomposition of x some high-energy materials, including ammonium dinitramide. The practical importance has motivated considerable theoretical interest in these reactions. We review numerous ab - initio molecular orbital studies of potential energy surfaces for NO NH and theoretical calculations of their kinetic parameters, such as x y thermal rate constants and branching ratios of various products. The most advanced theoretical calculations are carried out using the Gaussian-2 family of methods which provides the chemical accuracy (within 2 kcal mol ) for the energetics and molecular parameters of the reactants, products, intermediates and transition states. We present a detailed comparison of the theoretical results with available experimental data. We show that the reactions of NO with NH and NH x are very fast because they occur without a barrier and lead to the formation of multiple products which include radicals and stable molecules. The reactions of NO with NH, taking place by the H abstraction to form NH and HNO, are slow x x but still relevant to the NH de-NO system, because of their fast reverse processes x which have not yet been measured experimentally.