Stationkeeping of quasiperiodic orbits near a periodic halo orbit of the Earth+Moon-Sun system is analyzed. The full solar system is considered as a perturbation of the restricted three body problem. In the full solar system the periodic orbits are lost but the system still has quasi periodic solutions relatively close to the previous halo orbits. They are approximately obtained analytically and refined numerically. These orbits can be taken as nominal orbits for halo missions. They inherit the unstable character of the halo orbits. Although they are no longer periodic their invariant manifolds, which are approximated by analytical and numerical solutions of the variational equations, can be introduced. Simple geometrical considerations help to develop a very cheap stationkeeping algorithm.