Motion near the Lagrangean triangular points has been investigated by Rabe 1961, and Long periodic orbits have been established numerically in the circular case. i.e. when the two primaries revolve around the common çenter of mass in circular orbits. Following the same procedure as Rabe, Goodrich found short periodic orbits in the same case 1965. We showed, 1967, that one of the Rabes înitial Conditions also gives periodic orbit in the elliptic case. On the other hand Szebehely treated the elliptic case analyticaily. There are agreements between our numerical and Szebehely’s analytical results. an The restricted problem of three bodies studies the motion of infinitesimal partide moving under the influence of two finite point masses. It is assumed that the two bodies move about their çenter of mass in concentric circles and their orbits are undistur- bed by the infinitesimal third body.