  On a closed 4-dimensional Riemannian manifold, we give a lower bound for the
square of the first eigenvalue of the Yamabe operator in terms of the total
Branson's Q-curvature. As a consequence, if the manifold is spin, we relate the
first eigenvalue of the Dirac operator to the total Branson's Q-curvature. On a
closed n-dimensional manifold, $n\ge 5$, we compare the three basic conformally
covariant operators : the Branson-Paneitz, the Yamabe and the Dirac operator
(if the manifold is spin) through their first eigenvalues. Equality cases are
also characterized.
