  We present the results of Monte Carlo simulations of two different 10-state
Potts glasses with random nearest neighbor interactions on a simple cubic
lattice. In the first model the interactions come from a \pm J distribution and
in the second model from a Gaussian one, and in both cases the first two
moments of the distribution are chosen to be equal to J_0=-1 and Delta J=1. At
low temperatures the spin autocorrelation function for the \pm J model relaxes
in several steps whereas the one for the Gaussian model shows only one. In both
systems the relaxation time increases like an Arrhenius law. Unlike the
infinite range model, there are only very weak finite size effects and there is
no evidence that a dynamical or a static transition exists at a finite
temperature.
