The space orientation of the LAser GEO-dynamics Satellite (LAGEOS) spin axis evolves slowly in time due to a permanent influence of perturbing torques. We extend a theoretical model of this evolution by including two, previously neglected, effects: (i) a radiation torque due to an asymmetric reflectivity of the satellite surface, and (ii) a perturbing torque related to a possible miscentering between the mass and geometric centers of the satellite. We demonstrate that both effects will contribute importantly to the scenario of the LAGEOS spin axis evolution at the end of this decade, and could be detected by both direct measurements of the LAGEOS spin axis and orbit analysis. ¿ American Geophysical Union 1996