  Symmetric cones can be endowed with at least two interesting non Riemannian
metrics: the Hilbert and the Thompson metrics. It is trivial that the linear
maps preserving the cone are isometries for those two metrics. Oddly enough
those are not the only isometries in general. We give here a full description
of the isometry groups for both the Hilbert and the Thompson metrics using
essentially the theory of euclidean Jordan algebras. Those results were already
proved for the symmetric cone of complexe positive hermitian matrices by L.
Moln{\'a}r. In this paper however we do not make any assumption on the
symmetric cone under scrutiny (it could be reducible and contain exceptional
factors).
