  We have performed Monte Carlo simulations to determine current--voltage
characteristics of two different vortex glass models in two dimensions. The
results confirm the conclusions of earlier studies that there is a transition
at $T=0$. In addition we find that, as $T\to 0$, the linear resistance vanishes
exponentially, and the current scale, $J_{nl}$, where non-linearities appear in
the $I$--$V$ characteristics varies roughly as $T^3$, quite different from the
predictions of conventional flux creep theory, $J_{nl} \sim T$. The results for
the two models agree quite well with each other, and also agree fairly well
with recent experiments on very thin films of YBCO.
