The degree 1 deformations of Earth induced by a surface load are computed, in a reference frame related to the center of mass of the planet, using a theoretical approach (Love number formalism), at secular timescale, where Earth has a viscoelastic behavior. The temporal variation of the coordinates of the geocenter induced by the Pleistocenic deglaciation is investigated for two loading histories (three ice sheets with the same time dependence or ICE-3G model) testing different viscosity profiles within the mantle. The present-day secular variation of Earth's geocenter induced by postglacial rebound is found to be from 0.2 up to 0.5 mm/yr, and consequently, we suggest that observations from Space Geodesy of this rate could be used to constrain the viscosity contrast between upper and lower mantle. ¿ 2001 American Geophysical Union