  With unusually slow and high-resolution sweeps of magnetic field, strong,
ultra-narrow (width down to $100 {\rm \mu T}$) resistance peaks are observed in
the regime of breakdown of the quantum Hall effect. The peaks are dependent on
the directions and even the history of magnetic field sweeps, indicating the
involvement of a very slow physical process. Such a process and the sharp peaks
are, however, not predicted by existing theories. We also find a clear
connection between the resistance peaks and nuclear spin polarization.
