Abstract: The starting point is a process to improve the performance of the incineration of combustible waste material in an incineration chamber, whereby the waste material is conveyed to a burner flame where it is burned with combustion air at a temperature in the range from 1100° C. to 1700° C. [2012° F. to 3092° F.]. On this basis, in order to create a process that allows a capacity increase of installations employed for the exothermal incineration of waste materials, it is proposed according to the invention that at least part of the combustion air is replaced by an oxygen-rich gas having an oxygen content that is higher than that of air and that the oxygen-rich gas is mixed with a cooling medium.