This paper presents the results of a series of numerical simulations exploring the stability of fluid flow in vaneless diffusers of centrifugal compressors. Three-dimensional, time-dependent, Reynolds-averaged Navier-Stokes simulations were performed for a fixed diffuser width ratio. Effective flow angle was varied from simulation to simulation in order to predict the threshold angle at which the instability — rotating stall — is manifested and maintained. The predicted threshold angle or stability limit is in excellent agreement with experimental data. The simulations reveal a two-stall cell configuration at the threshold condition.