  We report on some unusual behavior of the measured current-voltage
characteristics (CVC) in artificially prepared two-dimensional unshunted array
of overdamped Nb-AlO_x-Nb Josephson junctions. The obtained nonlinear CVC are
found to exhibit a pronounced (and practically temperature independent)
crossover at some current I_{cr}=\left(\frac{1}{2\beta_C}-1\right)I_C from a
resistance R dominated state with V_R=R\sqrt{I^2-I_C^2} below I_{cr} to a
capacitance C dominated state with V_C=\sqrt{\frac{\hbar}{4eC}} \sqrt{I-I_C}
above I_{cr}. The origin of the observed behavior is discussed within a
single-plaquette approximation assuming the conventional RSJ model with a
finite capacitance and the Ambegaokar-Baratoff relation for the critical
current of the single junction.
