In view of the need of an accurate modelling of nongravitational forces on laser-tracked satellites, it is important to understand their rotational dynamics, which determines the temperature anisotropy and the ensuing radiation recoil effects. We propose a model of the torques acting on LAGEOS due the eddy currents and gravity gradient. The electromotive forces induced in the spacecraft by its rotation in the magnetic field on the Earth dissipate angular momentum and produce a precession of the spin axis; the oblate spacecraft will precess in the gravitational field of the Earth at a rate proportional to the rotation period. Therefore the gravitational torques become more and more important with time and eventually may produce a chaotic dynamics. The predicted evolution of the spin period agrees very well with the few experimental data available and corresponds to an approximately exponential growth rate of about 3 years. ¿American Geophysical Union 1990