  We analyze here the fluctuation conductivity in the vicinity of the critical
point in a 2D Josephson junction array shunted by an Ohmic resistor.We find
that at the Gaussian level, the conductivity acquires a logarithmic dependence
on $T/(T-T_c)$ when the dissipation is sufficiently small. In the renormalized
classical regime, this logarithmic dependence gives rise to a leveling-off of
the resistivity at low to intermediate temperatures when fluctuations are
included. We show, however, that this trend does not persist to T=0 at which
point the resistivity vanishes. The possible relationship of the leveling of
the resistivity to the low temperature transport in granlar superconductors is
discussed.
