Method for operating a gas burner, wherein during burner-on phases a defined gas/air mixture having a defined mixing ratio of gas and air is provided to a burner chamber of the gas burner for combusting the defined gas/air mixture within the burner chamber; said defined gas/air mixture is provided by a mixing device mixing an air flow provided by an air duct with a gas flow provided by a gas duct; said air flow flowing through the air duct is provided by fan in such a way that the fan speed of the fan depends on a desired burner load of the gas burner, wherein the fan speed range of the fan defines a modulation range of the gas burner in such a way that the modulation range of the gas burner is defined by an upper fan speed of the fan and a lower fan speed of the fan; said mixing ratio of gas and air of the gas/air mixture is controlled over the modulation range of the gas burner by a pneumatic controller on basis of a pressure difference between the gas pressure of the gas flow in the gas pipe and a reference pressure, wherein either the air pressure of the air flow in the air duct or the ambient pressure is used as reference pressure, and wherein the pressure difference between the gas pressure of the gas flow in the gas pipe and the reference pressure is determined and controlled pneumatically; during burner on phases the combustion quality is monitored permanently over at least a portion of the modulation range of the gas burner on basis of a signal provided by a combustion quality sensor; characterized in that the signal provided by the combustion quality sensor is used to detect tolerances of the pneumatic controller and/or a potentially changing behaviour of the pneumatic controller by checking if the combustion quality is inside or outside a defined combustion quality range, wherein when the combustion quality changes non-uniformly over the observed portion of the modulation range or the modulation range of the gas burner a change in the behaviour of the pneumatic controller is detected; that the modulation range is divided in a first subrange defined by the upper fan speed and an intermediate fan speed and in a second subrange defined by the intermediate fan speed and the lower fan speed, wherein the gas burner is controlled in such a way that for a heat demand requiring a fan speed within the first subrange of the modulation range the mixing ratio of gas and air of the gas/air mixture is kept constant over the first subrange of the modulation range and the fan speed is changed to the desired fan load within the first subrange of the modulation range of the gas burner, for a heat demand requiring a fan speed within the second subrange of the modulation range the combustion quality is checked at the intermediate fan speed or at a fan speed depending on the intermediate fan speed, wherein when the combustion quality at said fan speed for which the combustion quality is checked is inside the defined combustion quality range, the mixing ratio of gas and air of the gas/air mixture is kept constant, and the fan speed is changed to the desired fan speed within the second subrange of the modulation range of the gas burner; when the combustion quality at said fan speed for which the combustion quality is checked is outside the defined combustion quality range, the mixing ratio of gas and air of the gas/air mixture is changed by adjusting a setting of a gas throttle positioned within the gas duct so that influences of tolerances of the pneumatic controller and/or of a potentially changing behaviour of the pneumatic controller become compensated to broaden the second subrange modulation range, and the fan speed is changed to the desired fan speed within the second subrange of the modulation range of the gas burner. for a heat demand requiring a fan speed within the first subrange of the modulation range the mixing ratio of gas and air of the gas/air mixture is kept constant over the first subrange of the modulation range and the fan speed is changed to the desired fan load within the first subrange of the modulation range of the gas burner, for a heat demand requiring a fan speed within the second subrange of the modulation range the combustion quality is checked at the intermediate fan speed or at a fan speed depending on the intermediate fan speed, wherein when the combustion quality at said fan speed for which the combustion quality is checked is inside the defined combustion quality range, the mixing ratio of gas and air of the gas/air mixture is kept constant, and the fan speed is changed to the desired fan speed within the second subrange of the modulation range of the gas burner; when the combustion quality at said fan speed for which the combustion quality is checked is outside the defined combustion quality range, the mixing ratio of gas and air of the gas/air mixture is changed by adjusting a setting of a gas throttle positioned within the gas duct so that influences of tolerances of the pneumatic controller and/or of a potentially changing behaviour of the pneumatic controller become compensated to broaden the second subrange modulation range, and the fan speed is changed to the desired fan speed within the second subrange of the modulation range of the gas burner.