We study the changes of the long-wavelength portion of the Earth's gravity field as a result of present-day glacial discharges and the possible growth of the Antarctic ice sheet. We employ both Maxwell and Burger's body rheologies and find that there are significant differences in the responses between the two rheologies for time spans less than a century. Both present-day glacial forcing and the ice buildup on Antarctica can cause non-negligible perturbations in J˙2 of about one-third the observed amount. The contributions from the two mechanisms have opposite signs in J˙2 Only for l=3 and 6 do these cryospheric contributors act in concert with one another in distinguishing the gravity field. All other degree harmonics, up to l=9, have opposite signs from these two excitations. For a steady-state lower-mantle viscosity of 1022 Pa s, J˙3 can attain a maximum value of around 1.5¿10-11 yr-1 and J˙6 a value of -1.3¿10-11 yr-1 for current forcings. These have signs opposite to those predicted for Pleistocene deglaciation. All harmonics, up to l=9, are sensitive to variations of the steady-state viscosity in the lower mantle, even for time scales shorter than 100 years. It is proposed that detailed satellite monitoring of present-day ice movements in conjunction with geodetic satellite missions will eventually provide a viable alternative for estimating deep mantle viscosity, useful in mantle convection models. ¿ American Geophysical Union 1988