  Stochastic lattice gases with degenerate rates, namely conservative particle
systems where the exchange rates vanish for some configurations, have been
introduced as simplified models for glassy dynamics. We introduce two
particular models and consider them in a finite volume of size $\ell$ in
contact with particle reservoirs at the boundary. We prove that, as for
non--degenerate rates, the inverse of the spectral gap and the logarithmic
Sobolev constant grow as $\ell^2$. It is also shown how one can obtain, via a
scaling limit from the logarithmic Sobolev inequality, the exponential decay of
a macroscopic entropy associated to a degenerate parabolic differential
equation (porous media equation). We analyze finally the tagged particle
displacement for the stationary process in infinite volume. In dimension larger
than two we prove that, in the diffusive scaling limit, it converges to a
Brownian motion with non--degenerate diffusion coefficient.
