An analytical averaging theory founded on the elliptic restricted three-body problem and valid for libration motions shows that there are forbidden intervals in the distribution of the mean semi-major axes at the resonance (p+1) : p. The actual asteroids may cross these gaps but they cannot remain there. Some 15 of the presently known Hildas are in the gap and some of them may cross it completely. The Griquas are presently at the left of the gap but some of them periodically cross the gap.
Secular variations planetarj' theories constructed at the Bureau des Longitudes use either order by order methods (with respect to the masses) or iterative methods. In all cases, the convergence of the
solutions with respect to the masses is slackened by the upcoming of quasi resonant terms giving-smaller and smaller divisors. This shows how diflicult it is to get very precise solutions over long time spans such as several thousands of years. On another hand, if we locally develop the quasi resonant terms with respect to time, we can get very precise analytical solutions over reduced time spans. We have therefore undertaken an analytical solution for the time span 1950-2050, aiming at a 30 meter precision on the position of the Earth with respect to the barycenter of the solar system. This precision is in fact needed for the comparison to the millisecond pulsar data.