Over recent years considerable advances have taken place in the field of space geodesy, resulting in a number of highly precise global positioning techniques. The increased resolution of many of the scientific products from the new observational techniques has stimulated the interest of not only geodesists but also geophysicists. Furthermore, their potential to determine the orientation of the earth's axis of rotation (polar motion) and the variations of the rate of rotation of the earth about that axis, was recognised by the scientific community. The result was the establishment of Project MERIT, to intercompare these new observational techniques. Satellite Laser Ranging, a method of measuring the distance from a point on the earth's surface to an artificial satellite by means of timing the flight of a short pulse of laser light, is currently the most accurate available means of tracking near earth satellites. However, in order to reach the accuracy requirements of current geodetic applications dedicated satellites, such as the NASA LAser GEOdynamic Satellite (LAGEOS), must be tracked and specialised processing software must be used. This Thesis describes the basic theory behind the analysis of Satellite Laser Ranging Observations, with a special emphasis on the determination of earth rotation parameters (the polar motion and the variations in the rate of rotation). The development and testing, at Nottingham, of the Satellite Orbit Determination and Analysis Package Of Programs, SODAPOP, for the processing of laser range data, is described. The thesis also presents and discusses the results of the analysis of laser range observations the LAGEOS satellite, from the short and main campaigns of project MERIT.