We investigate the evolution of multiring basins on the Moon. The orbital geophysical and geochemical data collected by Lunar Prospector allow three distinct groups of basins to be identified. Group 1 basins show well-preserved topography, a bull's-eye gravity signature, and little mare basalt fill. Group 2 basins contain large amounts of mare basalt and show mare-dominated gravity and topography signatures. Group 3 basins are characterized by low-amplitude topographic relief and weak gravity anomalies. While the crustal structures of group 1 and 2 basins appear to date from the collapse of the transient cavity, group 3 basins are highly degraded and show very little crustal thinning. Using a viscoelastic model, we explore the evolution of the lunar multiring basins, with the goal of explaining the degraded condition of group 3 basins. Our results show that while viscous relaxation is a plausible explanation for the state of group 3 farside basins, requiring heat flux > 25--40 mW m-2, the thin nearside crust renders subsolidus ductile flow in the crust unlikely. The existence of many degraded basins on the nearside points to a weakened, and possibly partially molten, lower crust. That South Pole--Aitken appears not to have relaxed suggests that similar conditions did not exist there and that the nearside was hotter than the farside early on. This is likely a consequence of the nearside-farside crustal thickness dichotomy, which would have caused the farside to reach full crystallization first, leaving the nearside with the remaining liquid and an excess of heat-producing elements.