  We present a theory of the phonon-assisted nonlinear dc transport of 2D
electrons in high Landau levels. The nonlinear dissipative resistivity displays
quantum magneto-oscillations governed by two parameters which are proportional
to the Hall drift velocity $v_H$ of electrons in electric field and the speed
of sound $s$. In the subsonic regime, $v_H<s$, the theory quantitatively
reproduces the oscillation pattern observed in recent experiments. We also find
the $\pi/2$ phase change of oscillations across the sound barrier $v_H=s$. In
the supersonic regime, $v_H>s$, the amplitude of oscillations saturates with
lowering temperature, while the subsonic region displays exponential
suppression of the phonon-assisted oscillations with temperature.
