The High Temperature Air Combustion (HiTAC) regime, in which reactants are preheated prior to mixing and burning by recycled exhaust gases, has proven to be an attractive method for application in advanced industrial furnaces for energy saving and reduction of NOx emissions. In this technology, air diluted by nitrogen or combustion products can be preheated to high temperatures, while rich or lean methane/air mixtures can be injected into the preheated gases to realize diffusion or partially premixed combustion. The objective of the present study is to understand partially premixed lean or rich methane/air flames in counter-flow with preheated air in order to provide fundamental understanding of the physical and chemical processes that occur during this combustion mode. HiTAC is shown to improve fuel consumption, and to have the beneficial effect of low NOx emission when high temperature air with low concentration of oxygen is used. This study is based on a numerical modeling of an opposed flow diffusion flame with the Oppdif/CHEMKIN software using the detailed comprehensive (GRImech3.0) mechanism for the oxidation kinetics of methane. Two partially premixed flames (rich and lean methane/air mixture) are selected to simulate this combustion regime. Simulation results clearly illustrate that the flame structure for the rich partially premixed flame is significantly affected by the oxygen concentration in the air. For this flame, and with 5% oxygen content in the air, a significant reduction in NOx emission is observed, but this is accompanied by higher CO emissions. On the other hand, the results show that the low oxygen content in preheated air does not much affect the NOx emissions for the lean partially premixed flames.