  The influence of the motion of a magnetic-field-induced spin-density wave
(FISDW) on the quantum Hall effect in a quasi-one-dimensional conductor is
studied theoretically. In the ideal case of a free FISDW, it is found that the
counterflow of the FISDW precisely cancels the quantum Hall current, so the
resultant Hall conductivity is zero. In real systems, the Hall conductivity
should vanish at the high frequencies, where the pinning and the damping can be
neglected, and the dynamics of the FISDW is dominated by inertia.
