Abstract: The invention relates to a process for combustion of a fuel with an oxygen-rich oxidant, in a combustion chamber (3), in which, cyclically: at least one principal variable representing the combustion in the said combustion chamber (3) is measured, and, as a function of the result of the measurement of the at least one principal variable, a control instruction for regulating the flowrates of fuel and oxidant to be injected into the combustion chamber (3) is determined. Then the regulating control instruction is applied in order to make the fuel burn with the oxidant in the chamber (3). Additionally at least one secondary variable associated with an operational constraint of the combustion chamber (3) or with a perturbation in the operation of the latter is measured, and for the determination of regulating control instruction, the measurement result of the at least one secondary variable is also taken into account. The invention is useful in glass furnaces, rotary furnaces, and incineration furnaces.