A process for incinerating combustible materials including the steps of: delivering combustible material and inlet gases to a primary combustion chamber, the inlet gases having an oxygen content of at least 50 vol %; burning the combustible material with the oxygen of the inlet gases in the primary combustion chamber producing flue gases and solid particulates as thermal decomposition products of the burnt combustible material; passing the flue gases and particulates to a secondary combustion chamber where further combustion occurs; cooling the flue gases exiting the secondary combustion chamber; returning a portion of the cooled flue gases to at least one of the combustion chambers where the cooled gases moderate the temperature in the at least one chamber; and passing the remaining portion of cooled flue gases on to a flue gas purification system where pollutants in the flue gases and particulates are substantially converted to benign compounds or removed entirely before the flue gases are emitted into the atmosphere.