  Let f be a dominant meromorphic self-map on a compact Kaehler manifold X
which preserves a fibration given by a meromorphic map from X to a compact
Kaehler manifold Y. We compute the dynamical degrees of f in term of its
dynamical degrees relative to the fibration and the dynamical degrees of the
map g on Y which is induced by f. We derive from this result new properties of
some fibrations intrinsically associated to X when this manifold admits an
interesting dynamical system.
