  Let $(M,g)$ be a pseudo-Riemannian manifold. We propose a new approach for
defining the conformal Schwarzian derivatives. These derivatives are 1-cocycles
on the group of diffeomorphisms of $M$ related to the modules of linear
differential operators. As operators, these derivatives do not depend on the
rescaling of the metric $g.$ In particular, if the manifold $(M,g)$ is
conformally flat, these derivatives vanish on the conformal group
$\Og(p+1,q+1),$ where $\mathrm{dim} (M)=p+q.$ This work is a continuation of
[1,4] where the Schwarzian derivative was defined on a manifold endowed with a
projective connection.
