NO catalytic reduction on Ag/γ-Al 2 O 3 catalysts is a very promising process from the industrial and ecological perspective. Details of its mechanism, which are still not fully clear, have great importance for a deep understanding of various heterogeneous NO reduction processes. In this work, a thorough theoretical study of the mechanism of NO reduction on the Ag/γ-Al 2 O 3 catalyst is carried out. Two schemes of the mechanism for catalysts with different silver concentrations and, subsequently, with different reaction centers, are proposed. For the catalyst with a low silver content, a mechanism based on isocyanate species is proposed, while for catalysts with a high silver content, key intermediates are adsorbed NO dimers. The thermodynamic and kinetic feasibility of the proposed schemes is confirmed by density functional theory calculations of the reaction pathways both on isolated silver clusters and on the catalyst surface. These schemes explain the experimentally observed N 2 O or N 2 prevalence in the reaction products. Calculations of the catalyst surface are carried out within the original three-layer embedded cluster model, which provides accurate results of calculations of vibrational frequencies, geometries, and energy characteristics. The process of silver particle migration along the catalyst surface is studied. Energy barriers of migration are estimated. The influence of the catalytic center nature and presence of the aluminum oxide support on NO, N 2 , and N 2 O adsorption processes are studied, and the corresponding adsorption energies are calculated.