The relationship between the surface topography and gravitational potential of Venus and the Earth is investigated over the spherical harmonics of degree and order up to 75. The covarying harmonics of the topography and the potential, i.e. the harmonics having nonnegative degree/order correlation coefficients, are treated separately from the antivarying harmonics, those with negative degree/order correlation coefficients. The covarying harmonics provide reliable estimates of the compensation depth of the surface topography. The surface topography of the Earth specified by spherical harmonics of degree higher than 11 is essentially compensated isostatically at the Moho discontinuity, whereas the lower-degree harmonics are largely supported by mantle dynamics. For Venus the harmonics of degree lower than 9 are probably supported by mantle dynamics, while those of degree higher than 35 are most likely supported isostatically at a depth of about 45 km. There is a gradual increase in the compensation depth of the surface topography as the degree of harmonics decreases from 35 to 9, implying a combination of isostatic and dynamic support of these harmonics. Part of the topography specified by antivarying harmonics of degree greater than about 20 cannot be maintained by an isostatic compensation or a steady state dynamic support; it is more likely time dependent. Assuming that this part of the topography arises from viscous deformation of mantle under surface loading, the gravity and topography relationship provides a first-order estimate of 5¿1024 Pa s for the viscosity of the Venusian mantle. This high viscosity results in a Rayleigh number of about 12000 for the mantle, which is only about 17 times greater than the critical Rayleigh number for convection, implying a very slow quasi-steady convection in the mantle. ¿ American Geophysical Union 1996