Process for combusting, by means of a burner, a fuel with an oxidant in a combustion zone downstream of the burner, wherein the burner comprises: - a block with an entrance face opposite the combustion zone and an exit face on the side of the combustion zone and opposite the entrance face, said block comprising at least one first perforation that extends from the entrance face to the exit face and that ends at a first level in the exit face of the block, and at least one second perforation that extends from the entrance face to the exit face and that ends in the exit face at a second level spaced apart from the first level and located below or above the first level, - at least one fuel injector positioned in the at least one first perforation of the block, - at least one main oxidant injector positioned in the at least one second perforation of the block, process wherein: - at least one stream of the fuel is injected into the combustion zone through the at least one fuel injector and the at least one first perforation, - a main oxidant flow is introduced into the combustion zone in at least one main stream of the oxidant injected into the combustion zone below or above the at least one stream of the fuel and through the at least one main oxidant injector and the at least one second perforation, - an auxiliary flow of the oxidant is introduced in the combustion zone into contact with the at least one fuel stream so as to generate an initial flame by initial partial combustion of the fuel with the auxiliary flow of the oxidant in the combustion zone, - the oxidant of the at least one main stream of the oxidant mixes downstream of the initial flame with fuel that was not consumed by the partial combustion in the initial flame so as to complete the combustion of the fuel with the oxidant of the at least one main stream downstream of the initial flame, process wherein: - the emission intensity and optionally the oscillation frequency of the initial flame is measured, and - the flow rate of the main flow of the oxidant or the ratio between the flow rate of the main flow of the oxidant and the flow rate of the auxiliary flow of the oxidant is adjusted depending on the measured emission intensity and optionally the measured oscillation frequency. - a block with an entrance face opposite the combustion zone and an exit face on the side of the combustion zone and opposite the entrance face, said block comprising at least one first perforation that extends from the entrance face to the exit face and that ends at a first level in the exit face of the block, and at least one second perforation that extends from the entrance face to the exit face and that ends in the exit face at a second level spaced apart from the first level and located below or above the first level, - at least one fuel injector positioned in the at least one first perforation of the block, - at least one main oxidant injector positioned in the at least one second perforation of the block, - at least one stream of the fuel is injected into the combustion zone through the at least one fuel injector and the at least one first perforation, - a main oxidant flow is introduced into the combustion zone in at least one main stream of the oxidant injected into the combustion zone below or above the at least one stream of the fuel and through the at least one main oxidant injector and the at least one second perforation, - an auxiliary flow of the oxidant is introduced in the combustion zone into contact with the at least one fuel stream so as to generate an initial flame by initial partial combustion of the fuel with the auxiliary flow of the oxidant in the combustion zone, - the oxidant of the at least one main stream of the oxidant mixes downstream of the initial flame with fuel that was not consumed by the partial combustion in the initial flame so as to complete the combustion of the fuel with the oxidant of the at least one main stream downstream of the initial flame, - the emission intensity and optionally the oscillation frequency of the initial flame is measured, and - the flow rate of the main flow of the oxidant or the ratio between the flow rate of the main flow of the oxidant and the flow rate of the auxiliary flow of the oxidant is adjusted depending on the measured emission intensity and optionally the measured oscillation frequency.