  We investigate the long time stability in Nekhoroshev's sense for the
Sun-Jupiter-Saturn problem in the framework of the problem of three bodies.
Using computer algebra in order to perform huge perturbation expansions we show
that the stability for a time comparable with the age of the universe is
actually reached, but with some strong truncations on the perturbation
expansion of the Hamiltonian at some stage. An improvement of such results is
currently under investigation.
