A combined analytical-numerical procedure for determining precise mean orbital elements is presented and applied to the orbits of GEOS-1 and GEOS-2. The precision of the mean semi-major axes of these orbits is a few tens of centimeters when optical flash data is used to determine two-day orbital arcs. Four-day Minitrack orbits give mean semi-major axes of a few meters precision. The mean orientation parameters are obtained to a precision of about 0.1 sec (about 3m) or better from the optical orbits. This precision is adequate for determinations of tidal parameters, particularly in the case of GEOS-2, where the tidal perturbation of the inclination is 10 sec.