We prove, under suitable non-resonance and non-degeneracy ``twist''
conditions, a Birkhoff-Lewis type result showing the existence of infinitely
many periodic solutions, with larger and larger minimal period, accumulating
onto elliptic invariant tori (of Hamiltonian systems). We prove the
applicability of this result to the spatial planetary three-body problem in the
small eccentricity-inclination regime. Furthermore, we find other periodic
orbits under some restrictions on the period and the masses of the ``planets''.
The proofs are based on averaging theory, KAM theory and variational methods.
(Supported by M.U.R.S.T. Variational Methods and Nonlinear Differential
Equations.