This monograph presents an application of the first- order conditional moment closure (CMC) approach to modelling turbulent non-premixed flames of methane, propane and ethylene, with particular attention given to sooting flames. One objective of the current research is to investigate the practicability of incorporating gas-phase chemical mechanisms of varying length and complexity into calculations of turbulent non-premixed flames. Another objective is to extend the current scope of CMC combustion modelling by incorporating calculations of detailed gas-phase chemistry, soot formation and oxidation, and radiative heat transfer. Overall, predictions are in far better accord with experimental data when differential diffusion is accounted for in the model, and realistic prediction of soot levels are not possible without the incorporation of such effects. Given the simplicity and relative accuracy of the model described, it offers potential for future development to cover a wide range of hydrocarbon fuels, including the high hydrocarbons used in practical combustors, as well as for application in complex combustor''s geometries.