The Galactic orbits of several families of stars, each of 40 stars, were computed in the mass model of innanen (1966) for a time of 5.0X 10 yr. The members of each family have the same energy and angular momentum. The 40 stars in each family were initially set flying apart near the sun. Their subsequent positions were compared as a function of time to determine whether the stars came to within 2 kpc of each other. in all cases, close approaches of short duration were found after every complete revolution around the Galaxy. For a group of stars whose initial motions are at a high inclination to the Galactic plane, close approaches of less than 250 pc were recorded, with the stars traveling in the same direction. The stars were found to lie on smooth curves like beads on a string which change in a consistent manner during each revolution around the Galaxy. This gives the possibility of the precise prediction of orbital behavior of stars of this class. A further family of orbits was investigated by considering stars escaping from a hypothetical globular cluster. No coalescences were found except for a slight tendency to congregate near their perigalactica.