Method of operating a long direct-fired inclined counterflow rotary kiln for the thermal treatment of material, the rotary kiln presenting a longitudinal axis around which the kiln rotates, said longitudinal axis being inclined with respect to the horizontal plane and extending longitudinally between an upper inlet end and a lower outlet end of the kiln, the kiln having an internal length Lint of from 20m to 100m and an internal diameter Dint and presenting a ratio Lint/Dint from 10 to 100, method: • whereby material to be treated is introduced into the kiln at the inlet end and is subjected to thermal treatment within the kiln, after which the treated material is evacuated from the kiln at the outlet end, • whereby a main fuel and a main oxidant are introduced into the kiln at the outlet end so as to generate a main combustion of the main fuel with the main oxidant, said main combustion taking place in a main combustion zone inside the rotary kiln extending over a distance of 1⁄4 to 1/3 of the internal length L int of the kiln from the outlet end, • whereby combustion gases generated by said main combustion travel through the kiln from the main combustion zone towards the inlet end through a heat exchange zone in which no combustion takes place and in which heat is transferred from the combustion gases to the material travelling in counterflow with the combustion gases, said heat exchange zone being located upstream of the main combustion zone, the combustion gases leaving the main combustion zone optionally containing combustible substances generated by an incomplete main combustion of the main fuel, • whereby the combustion gases generated by said main combustion are evacuated from the kiln via a flue gas outlet situated at the inlet end of the kiln, and • whereby supplementary oxidant and optionally also supplementary fuel are introduced into the kiln at the inlet end, the method being characterized in that: • the supplementary oxidant introduced into the kiln has an oxygen content of from 50%vol to 100%vol, preferably at least 80%vol, more preferably at least 90%vol and most preferably at least 97%vol, • the supplementary oxidant and, if introduced into the kiln, the supplementary fuel are introduced into the kiln at the inlet end so as to combust any combustible substances present in the combustion gases from the main combustion zone and, if introduced into the kiln, the supplementary fuel with the supplementary oxidant in a supplementary combustion zone inside the rotary kiln which extends over a distance from the inlet end of at most % of the internal length L int, so that the combustion gases generated by the supplementary combustion are evacuated together with the combustion gases generated by the main combustion via the flue gas outlet of the kiln • whereby material to be treated is introduced into the kiln at the inlet end and is subjected to thermal treatment within the kiln, after which the treated material is evacuated from the kiln at the outlet end, • whereby a main fuel and a main oxidant are introduced into the kiln at the outlet end so as to generate a main combustion of the main fuel with the main oxidant, said main combustion taking place in a main combustion zone inside the rotary kiln extending over a distance of 1⁄4 to 1/3 of the internal length L int of the kiln from the outlet end, • whereby combustion gases generated by said main combustion travel through the kiln from the main combustion zone towards the inlet end through a heat exchange zone in which no combustion takes place and in which heat is transferred from the combustion gases to the material travelling in counterflow with the combustion gases, said heat exchange zone being located upstream of the main combustion zone, the combustion gases leaving the main combustion zone optionally containing combustible substances generated by an incomplete main combustion of the main fuel, • whereby the combustion gases generated by said main combustion are evacuated from the kiln via a flue gas outlet situated at the inlet end of the kiln, and • whereby supplementary oxidant and optionally also supplementary fuel are introduced into the kiln at the inlet end, • the supplementary oxidant introduced into the kiln has an oxygen content of from 50%vol to 100%vol, preferably at least 80%vol, more preferably at least 90%vol and most preferably at least 97%vol, • the supplementary oxidant and, if introduced into the kiln, the supplementary fuel are introduced into the kiln at the inlet end so as to combust any combustible substances present in the combustion gases from the main combustion zone and, if introduced into the kiln, the supplementary fuel with the supplementary oxidant in a supplementary combustion zone inside the rotary kiln which extends over a distance from the inlet end of at most % of the internal length L int, so that the combustion gases generated by the supplementary combustion are evacuated together with the combustion gases generated by the main combustion via the flue gas outlet of the kiln