There is a demand for further reducing NOx emissions from natural gas burners in heat and power production. For this issue, computational fluid dynamics (CFD) is a powerful tool, gaining in importance. However, because of computational efforts, there is the necessity for simplified models in order to simulate the combustion reactions and the NOx formation, respectively. In this work, different simplified models for the NOx formation, i.e., thermal NO and prompt NO formation, are validated against the predictions of a detailed chemical kinetic mechanism. NOx formation from CH4 combustion becomes relevant above similar to 1200 degrees C. For temperatures > 1600 degrees C, thermal NO formation is dominant. At lower temperatures, the N2O/NO and NNH routes have a significant contribution. For the conditions investigated, prompt NO formation is not relevant except for fuel-rich combustion. The simplified models capture thermal NO formation quite well. The superequilibrium radical concentration in the flame zone can be modeled by the "partial equilibrium approach" for the O radical, assuming its concentration in the relevant temperature range is similar to 30% higher than that for the equilibrium approach. However, this model overestimates NO formation under postflame conditions. For the prompt NO, model, CH4 and O-2 concentrations are necessary. These are obtained from the combustion model, which can be a local thermodynamic equilibrium (mixing rate limiting), a global reaction (reaction and/or mixing rate limiting), or a simplified reaction mechanism (flamelet model(1)). The prompt NO model based on these combustion calculations is able to reasonably capture the NO emissions predicted by the detailed mechanism. However, the performance of the prompt NO model is rather dependent on the combustion model. Thus, this one must be chosen carefully. Critically, it has to be stated that, although the simplified prompt NO model captures the observed trends acceptably, it lacks a physical basis. It assumes the prompt NO formation to be proportional to the fuel concentration. The detailed reaction mechanism shows that the NO formation is more strongly related to the fuel oxidation rate, i.e., the radical concentration. Moreover, the detailed mechanism shows that prompt NO formation is of secondary relevance. Low-temperature NO formation is more related to the N2O/NO and the NNH routes.