Lowering emissions from power generating gas turbines, while retaining efficiency and power output, constitutes a formidable task, both at fundamental and technical levels. Combined gas turbine cycles involving air humidification are particularly attractive, since they provide additional power with improved efficiency. Water or steam addition promotes the reduction of nitrogen oxides emissions, for both the premixed and non-premixed modes of operation. Consequently, there is an urgent need for thorough understanding of the combustion chemistry and flow-chemistry interaction under high pressure and high humidity conditions as well as simulating the turbulent flow field with realistic chemistry. Both objectives require the development of reduced kinetic mechanisms. Reduced mechanisms for methane combustion valid for high pressure and high humidity are developed here, using the CSP (computational singular perturbation) method. The effects of humidity and pressure on the dynamics of NO formation pathways are discussed. A reaction progress variable model for the simulation of turbulent combustion is also developed, valid for adiabatic, non-adiabatic, premixed as well as partly or non-premixed combustion of various fuels, including natural gas, hydrogen and syngas. The model utilizes the CSP methodology for accurate mapping of the pertinent thermochemical data on a set of two reaction progress variables. Preliminary results are displayed.