Low-threshold spontaneous pulsations are known to occur in the output beams of certain high-gain gas lasers, and good agreement between the experimental observations and numerical models has been achieved. There have also been several analytical studies of threshold criteria for spontaneously pulsing lasers. However, the analytical studies are mostly not applicable to the lasers in which the pulsations have been observed. Stability criteria for high-gain gas lasers are derived in this study, and these criteria are compared with a previously modeled gas laser instability.