  Current-voltage $I-V$ curves have been carefully measured for
YBa$_2$Cu$_3$O$_{7-\delta}$ thin films by following different thermal or field
annealing procedures. Although all data can be described quite well by the
vortex-glass theory, it is found that the dissipation in a small region just
above the vortex-glass transition is history dependent: the dissipation in the
warming up or field-increasing process is larger than that in the cooling down
or field-decreasing process. We attribute this history dependent dissipation to
possible existence of a slush vortex phase.
