  We discuss the final stages of double ionization of atoms in a strong
linearly polarized laser field within a classical model. We propose that all
trajectories leading to non-sequential double ionization pass close to a saddle
in phase space which we identify and characterize. The saddle lies in a two
degree of freedom subspace of symmetrically escaping electrons. The
distribution of longitudinal momenta of ions as calculated within the subspace
shows the double hump structure observed in experiments. Including a symmetric
bending mode of the electrons allows us to reproduce the transverse ion
momenta. We discuss also a path to sequential ionization and show that it does
not lead to the observed momentum distributions.
