  We study compact connected pseudo-Riemannian manifolds $(M,g)$ on which the
conformal group $\operatorname{Conf}(M,g)$ acts essentially and transitively.
We prove, in particular, that if the non-compact semi-simple part of
$\operatorname{Conf}(M,g)$ is the M{\"o}bius group, then $(M,g)$ is conformally
flat.
