The turbulent flow and combustion process of oxy-fuel flames are studied in the wake behind a burner rim separating fuel and oxidiser inlet channels. A range of conditions was considered, from stably attached flames, via lifted flames to blow-off. It was found that thechemical equilibrium model did not predict the chemical composition well. The laminar flamelet model performed better. It appeared that extinction is not the mechanism that leads to a lifted flame and therefore partial premixing was considered. It appeared that lifted oxy-fuel flames can be predicted fairly well by adjusting a turbulent burning velocity constant.