Gradient-driven Rayleigh-type instabilities in Hall plasma thrusters are analyzed using linearized two-fluid hydrodynamic equations. Necessary instability conditions and a general criterion for stability of azimuthally propagating perturbations are derived. For a simplified model of the axial distribution of parameters inside the thruster channel, the growth rate of an unstable wave, resonant with the azimuthal electron flow, is obtained. The frequency and phase relations are related to the results of experimental investigations of high-frequency oscillations in Hall thrusters.