A gas turbine apparatus is provided wherein a turbine is driven or rotated by burning a mixture of a fuel and compressed air and supplying a combustion gas generated by the combustion. A flameout determination unit is provided in the apparatus which is adapted to calculate the air/fuel ratio in the air/fuel mixture, correct the calculated air/fuel ratio to calculate a corrected air/fuel ratio which is substantially constant, compare the calculated corrected air/fuel ratio with a predetermined reference air/fuel ratio, and generate a signal indicative of occurrence of a flameout when the corrected air/fuel ratio is smaller than the reference air/fuel ratio. The corrected air/fuel ratio is calculated by calculating a deviation of a compressor discharge pressure of the compressed air from an air compressor, from a predetermined reference pressure, multiplying the pressure deviation by a predetermined constant, and adding the pressure deviation multiplied by the predetermined constant to the calculated air/fuel ratio. In this way, the corrected air/fuel ratio can be maintained substantially constant even if a load increases in steps.