Since LAGEOS was launched in May 1976, precise laser observations of the satellite have been used to estimate relative station positions, polar motion and the earth's gravitatonal constant. This work was accomplished with a model of the orbit dynamics that was adequate to compute trajectories of meter level accuracy for periods of 30 days in length. Our knowledge of the long-term evolution of the LAGEOS orbit has now been improved by an analysis of the ranging data collected during the first two years and eight months of the mission. Revisions to the originally adopted force model suggested by this work are presented in the form of the time-histories of individual Keplerian elements. Some unexpected variations in LAGEOS orbital period are observed and clear signatures in the inclination history of this satellite, which are predominantly caused by earth and ocean tidal effects, are also described. The motion of the ascending node of the orbit suggests short-term precisions of 1 or 2 hundredths of an arcsecond, equivalent to about a millisecond in Universal Time.