A method for operating a premix gas burner wherein an air flow rate and/or a fuel gas flow rate are controlled so as to generate heat with the premix burner in accordance with a heat demand related value. The fuel gas comprises hydrogen and the method further provides a desired air excess factor relation of the air/fuel gas mixture which defines the relation between a desired air excess factor and an input variable like the heat demand related value, an air flow rate related value, or a fuel gas flow rate related value. The desired air excess factor is not a constant factor but varies for different input variable values. The fuel gas flow rate and/or the air flow rate are controlled such that an actual air excess factor converges towards the desired air excess factor while meeting the heat demand.