A model for explaining the anomalous eccentricity excitations of the orbit of the LAGEOS I satellite is considered. It is suggested that two phenomena are responsible for the major part of these residuals: (1) about 1.3% mismodeling of the LAGEOS I surface mean radiation pressure coefficient, and (2) the Yarkovsky-Schach thermal effect with a properly modeled evolution of the satellite spin axis. Minor influences are also attributed to the asymmetric reflectivity of the satellite surface and the asymmetric thermal emissivity of the Earth. For these cases we give a suitable and compact formulation for the long-term orbit analysis. It is argued that contrary to the case of the LAGEOS I along-track residuals adjustment, which does not allow the determination of a particular combination of the Yarkovsky-Schach effect parameters, the combined analysis of the along-track residuals and the eccentricity excitations allows for their decorrelation. The resulting value of the Yarkovsky-Schach amplitude is estimated to be approximately 241 pm/s2, more than twice as large as given in previous works. In view of the unexplained part of the eccentricity residuals, we discuss the possible importance of several other nongravitational effects (Yarkovsky thermal effects due to Earth's heating, electromagnetic effects, mismodeling of the transitions through Earth's penumbra), concluding that none of them is quantitatively a good candidate.¿ 1997 American Geophysical Union