Recent experimental data suggest the formation of two new compounds, namely, Li4NH and Li1.5NH1.5, during the hydrogenation process of Li3N. The formation of these compounds could modify the hydrogen absorption and desorption characteristics of Li3N. We present here the results of our density functional theory calculations concerning their formation. We find that the direct hydrogenation reaction of Li3N to Li2 NH is predominantly favored but the formation of Li4NH is possible through the direct formation involving Li3N and LiH with an enthalpy of reaction much less negative than for the direct formation of Li2NH. The formation of this compound through the release of ammonia is not possible. This compound readily reacts with H2 exothermically with an enthalpy of reaction less negative than for the direct process. We also find that the formation of the intermediate phase Li2−xNH1+x for x=0.5 between imide (x=0) and amide (x=1) is possible. Li1.5NH1.5 is found to form in a cubic Li-vacant-type compound. After full relaxations of several structural models, the Li1.5NH1.5 compound presents a coexistence of ordered [NH]2− and [NH]2− anions. These results are discussed in terms of an analysis of the electronic structures of these compounds.