Abstract: In order to regulate the combustion air flow rate of a flue gas collection device (1) of a metallurgical reactor (2) comprising a combustion chamber (4) supplied with air by a variable flow fan (9), a set value C.sub.0 for the oxygen content in the flue gases in the discharge duct (5) is set, the oxygen content M.sub.1 of the flue gases at the outlet of the combustion chamber (4) is measured, using C.sub.0 and M.sub.1, a setting C.sub.1 for varying the combustion air flow rate is calculated, a variable representative of the sudden variations of the flow rate of unburnt gases at the outlet of the metallurgical reactor (2) is measured and a setting C.sub.2 for the combustion air flow rate is calculated to achieve complete combustion of the unburnt gases in the flue gases; the values C.sub.1 and C.sub.2 are added to obtain a setting for the combustion air flow rate which is sent to the regulation device of the fan (9); these calculations may be carried out by electronic means (14, 15, 16).