  We have investigated the I-V characteristics of strongly disordered
ultra-thin films of {\it Bi} and {\it Sn} produced by quench-condensation. Our
results show that both these sytems can be visualized as strongly disordered
arrays of Josephson junctions. The experimentally observed I-V characteristics
of these films is hysteretic, when the injected current is ramped from zero to
critical current and back. These are remarkably similar to the hysteretic I-V
of an underdamped single junction. We show by computer simulations that
hysteresis can persist in a very strongly disordered array. It is also possible
to estimate the individual junction parameters ($R$, $C$ and $I_c$) from the
experimental I-Vs of the film using this model. The films studied are in a
regime where the Josephson-coupling energy is larger than the charging energy.
We find that a simple relation $I_c(T)=I_c(0)(1-(T/T_c)^4)$ describes the
temperature dependence of the critical current quite accurately for films with
sheet resistance $\sim$ 500$\Omega$ or lower. We also find evidence of a
vortex-unbindi
