Numerical modelling of oxy-natural gas flames is a challenging task due to the large amount of radicals and intermediate species present in these flames. At the high temperature prevailing in oxy-natural gas flames, most of the chemical processes are extremely fast. Therefore, it can be assumed that mixing is the rate limiting factor and that all reactions can be treated as reversible. In this paper a mathematical model for computing oxy-natural gas flames has been developed. The turbulent combustion sub-model uses the Eddy Dissipation Concept whilst the chemistry is processed using a full equilibrium procedure. The model predictions have been compared with both detailed in-flame measurements of nine oxy-natural gas flames and flame predictions obtained using a mixed-is-burned model. The in-flame measurements were carried out at a thermal input of 1 MW, under conditions of both high and low heat extraction (water-cooled and refractory lined furnace). Both coaxial jet flames and staged flames were investigated. Results show that good predictions have been obtained with both combustion models, especially for the fluid dynamics and main chemical species (oxygen, carbon dioxide). In all the flames predicted, the equilibrium model showed to be superior to the mixed-is-burned model. The temperature and species concentration fields, including CO and NO, are better predicted since the effect of molecular dissociation has been accounted for. Moreover, the mathematical model has provided very useful insight into understanding the relation between NO, emissions and jet momentum.