Analytic solutions are determined for the optimum correction of all six elements of elliptic satellite orbits with low-thrust, power-limited propulsion systems. The optimum direction and magnitude of thrust are determinedas functions of time so as to minimize the fuel required to rendezvous in a given time or to minimize the fuel required for station keeping in the presence of known perturbations. The motion of the vehicle under the action of the optimum thrust program is also determined analytically. The solutions obtained are divided into two classes, depending on whether rendezvous requires few or many revolutions. In the latter case, simple analytic solutions are obtained explicitly by neglecting short-period perturbations.