We have studied the nonlinear conductivity of two-dimensional Coulomb glasses. We have used a Monte Carlo algorithm to simulate the dynamic of the system under an applied electric field E. We have compared results for two different models: a regular square lattice with only diagonal disorder and a random array of sites with diagonal and off-diagonal disorder. We have found that for moderate fields the logarithm of the conductivity is proportional to
, reproducing experimental results. We have also found that in the nonlinear regime the site occupancy in the Coulomb gap follows a Fermi-Dirac distribution with an effective temperature Teff higher than the phonon bath temperature T.