Periodic orbits of the bicircular problem and their stability; numerical simulations of the motion in an extended neighborhood of the triangular libration points in the Earth-Moon system; the equations of motion; periodic orbits of intermediate equations; a semianalytical approach to the quasi-periodic solution of the global equations; numerical determination of suitable orbits of the simplified system; and relative motion of two close spacecraft are discussed. There is evidence that orbits moving in a large annulus around L4 and L5 exist, that these orbits have small components out of the plane of the Earth-Moon system, and that they are at most mildly unstable.