Linear models for oscillator noise predict an improvement in frequency stability with increasing Quality factor. Although it is well known that this result does not apply to non-linear oscillators, systematic experimental investigations of the impact of damping on frequency stability of non-linear MEMS oscillators has not been previously reported. This paper studies the frequency stability of a nonlinear MEMS oscillator under variable damping conditions. Analytical and experimental investigation of a MEMS square-wave oscillator embedding a double-ended tuning fork resonator driven into the non-linear regime is introduced. The experimental results indicate that for a pre-set drive level, the variation of air-damping changes the onset of nonlinear behaviour in the resonator, which not only impacts the output frequency but also the phase/frequency noise of a nonlinear MEMS square wave oscillator. The random walk frequency noise and flicker frequency noise levels are strongly correlated with the non-linear operating point of the resonator, whereas the white phase and white frequency noise levels are impacted both by the output power and by operative nonlinearities.