We develop a self-consistent model for the evolution of the spin axis of LAGEOS and the related long-term semimajor axis perturbations, due to asymmetric emission/reflection of radiation from the satellite's surface. We show that the theory developed by Bertotti and Iess <1991> for the evolution of LAGEOS's rotation under magnetic and gravitational torques, which we have somewhat generalized here, can lead to a successful fit of the observed semimajor axis residuals, provided the correct initial conditions for the direction of the spin axis are chosen. The remaining residuals have a rms dispersion of 0.50¿10-12 m/s2, comparable to that of previous solutions, based on purely empirical fits of the spin axis direction as a function of time. The spectrum of the residuals indicates that they are probably due to unmodeled radiation forces (e.g., from Earth albedo and/or penumbra passages). Our solution allows us to predict the future evolution of LAGEOS's rotation for about another decade in the future, until the spin rate will become so slow that some basic assumptions of the theory will fail. A similar model can also be used to model/predict the coupled spin-orbit evolution of the LAGEOS II satellite, launched in late 1992, although the available data still cover a span of time too short for reaching significant quantitative conclusions concerning this satellite. ¿ American Geophysical Union 1996