  Compact pseudo-Riemannian manifolds that have parallel Weyl tensor without
being conformally flat or locally symmetric are known to exist in infinitely
many dimensions greater than 4. We prove some general topological properties of
such manifolds, namely, vanishing of the Euler characteristic and real
Pontryagin classes, and infiniteness of the fundamental group. We also show
that, in the Lorentzian case, each of them is at least 5-dimensional and admits
a two-fold cover which is a bundle over the circle.
