This paper shows improved phase-noise performance of MEMS oscillators when the sustaining amplifier operates a lateral bulk acoustic wave AlN-on-Si resonator in the nonlinear regime. An empirical exponential-series-based model that closely describes the phase noise in nonlinearity is presented, reflecting the increased resonator filter order and the reduced amplifier flicker-noise contribution. An oscillator using a 23 MHz in-plane shear mode resonator with a quality factor of 4,000 exhibits a phase noise of -130 dBc/Hz at 1 KHz offset-frequency, corresponding to an improvement of about 20 dB with respect to linear operation.