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Combustion of fuels with high-temperature air and large quantities of flue gas is perhaps the most rapidly developing combustion technology of the last decade. In this thesis this technology is named MILD combustion (Moderate and Intensive Low Oxygen Dilution). The technology, when applied together with an efficient heat recovery system, offers substantial energy savings and drastic reduction in CO2, CO and NO(x) emissions. The objective of the thesis is to perform an complete analysis of MILD combustion of natural gas with emphasis placed on NO(x) formation and destruction. The analysis is based on the experiments carried out at the IFRF (International Flame research Foundation) and the mathematical modeling work presented in this thesis. The goal is to examine whether the current generation of mathematical models can predict the characteristics of this novel combustion technology. Two types of mathematical models have been used in this thesis. A number of CFD-based models with several sub-models for turbulence-chemistry interactions belong into the first type. The models differ in turbulence modeling and in description of both combustion chemistry and NO(x) formation mechanics. These CFD-based RANS models (Reynolds Averaged Navier-Stokes) privilege the fluid dynamics over the chemistry calculations. A reactor network model that simplifies th fluid dynamics but accounts for comprehensive chemistry belongs to the second type of models used. This model has been applied to study the hydrocarbon chmbustion chemistry and nitrogen chemistry in MILD combustion. The IFRF experiments focused on some selected process parameters only and a more complete picture of the MILD combustion has been obtained by the mathematical modeling work presented in the thesis. The experimental burner features a strong (high momentum) comburent jet and two weak (low momentum) natural gas jets. Numerous publications have shown the inability of various RANS models to predict the structure of the weak jets. It has been postulated that new mechanisms fpr hydrocarbon combustion are needed to predict the thermal and chemical properties of these jets. In this thesis it has been shown that the failure is in error predictions of the entrainment and therefore is not related to any chemistry sub-models as has been postulated. It has been proven that the fluctuations due to the turbulent field do not play an important role. The reactor network has identified the prompt route as the dominant NO-formation mechanism with most of the NO being formed in the thin elongated region located at the interception of the natural gas jets and the comburent jet, and downstream in the furnace. The thermal route is strongly suppressed by the relative low level of the temperature in the furnace. An efficient NO-reburning process is present in the MILD combustion. Other mechanisms, like N2O and NNH, are of negligible importance. Several RANS-based models equipped with various NO-postprocessors have been used in this study and all of them predicted well the furnace NO-emissions. However, they have failed in identifying the correct NO formation and destruction mechanisms.