Vibration characteristics of a self-oscillating two-layer vocal fold model with left-right asymmetry in body-layer stiffness were experimentally and numerically investigated. Two regimes of distinct vibratory pattern were identified as a function of left-right stiffness mismatch. In the first regime with extremely large left-right stiffness mismatch, phonation onset resulted from an eigenmode synchronization process that involved only eigenmodes of the soft fold. Vocal fold vibration in this regime was dominated by a large-amplitude vibration of the soft fold, and phonation frequency was determined by the properties of the soft fold alone. The stiff fold was only enslaved to vibrate at a much reduced amplitude. In the second regime with small left-right stiffness mismatch, eigenmodes of both folds actively participated in the eigenmode synchronization process. The two folds vibrated with comparable amplitude, but the stiff fold consistently led the soft fold in phase for all conditions. A qualitatively good agreement was obtained between experiment and simulation, although the simulations generally underestimated phonation threshold pressure and onset frequency. The clinical implications of the results of this study are also discussed.