We evaluate the hypothesis that viscous relaxation has been an important process for modifying the topographic profiles of ancient large impact basins on the moon. We adopt a representative topographic profile of the Orientale basisn, the youngest large impact basin on the moon, as an estimate of the initial topography of older basins of similar horizontal dimensions, and we predict the topographic profiles that would result from viscous relaxation according to a number of simple analytical representation of the rheological response of the moon to surface topography. At wavelengths greater than the thickness of a high-viscosity lithosphere, both a decrease in viscosity with depth and the partial to complete isostatic compensation of topographic relief have pronounced effects on the wavelength-dependent relaxation times and must be considered in modeling viscous relaxation for features as large as impact basins. The effect of a decrease in viscosity with depth is to enhance the rate of viscous relaxation at long wavelengths, while the rate of relaxation decreases substantially for the fraction of long-wavelength topography which is isostatically compensated as an initial condition. These models are applied to two pre-Nectarian basins on the moon, the Tranquillitatis basin on the lunar nearside and the much larger and older South Pole-Aitken basin on the farside. The topographic profile of Tranquillitatis, after correcting for the effect of more basalt fill, is consistent with significant viscous relaxation of relief prior to the oldest episode of mare volcanism preserved as a surface unit. The large topographic relief of the larger farside basin, on the contrary, is not consistent with significant viscous relaxation and implies a mean crustal viscosity at least a factor of 10 higher than for the central nearside over the time interval during which substantial viscous relaxation of older nearside basins such as Tranquillitatis probably occurred. A difference in typical crustal temperature profiles between the farside and nearside is the most likely explanation of such a viscosity difference; such a nearside-farside asymmetry in near-surface temperature may date from the time of crust-mantle differentiation and may have persisted because of the different histories of late-stage impact basin formation and mare volcanism on the two hemispheres.