A numerical study of oxy-fuel combustion has been carried out in the pressure range of 0.1-3 MPa with methane as the fuel and carbondioxide-diluted oxygen with trace amount of nitrogen (termed here as c_air) as the oxidant. The flame structure and NO generation rate have been calculated using the flamelet model with the detailed GRI 3.0 mechanism for two oxygen concentrations of 23.3% and 20% by weight in the oxidant at a strain rate of 40 s(-1) (corresponding to a scalar dissipation rate of 1 s(-1)). It is observed that, for the reference case of 23.3 wt.% of oxygen, as the pressure increases, the peak temperature of the flame increases rapidly up to a pressure of 0.5 MPa, and more gradually at higher pressures. The concentrations of important intermediate radicals such as CH3, H and OH decrease considerably with increasing pressure while NO concentration follows the same trend as the temperature. Reducing the oxygen concentration to 20% by weight leads to an order of magnitude reduction in NO concentration. Also, for pressures greater than 0.3 MPa, the NO concentration decreases with increasing pressure in spite of the increasing peak flame temperatures. This can be attributed to the increasing domination of recombination reactions leading to less availability of the intermediate radicals H and OH which are necessary for the formation of NO by the thermal route. It is concluded that a stable, low NO, oxy-fuel flame can be obtained at high pressures at slightly increased dilution of oxygen. (C) 2008 Elsevier Ltd. All rights reserved.