Radial spacing between concentric rings of impact basins that lack central peaks is statistically similar and nonrandom on the Moon, Mercury, and Mars, both inside and outside the main ring. One spacing interval, (2.0 ?? 0.3)0.5D, or an integer multiple of it, dominates most basin rings. Three analytical approaches yield similar results from 296 remapped or newly mapped rings of 67 multi-ringed basins: least-squares of rank-grouped rings, least-squares of rank and ring diameter for each basin, and averaged ratios of adjacent rings. Analysis of 106 rings of 53 two-ring basins by the first and third methods yields an integer multiple (2 ??) of 2.00.5D. There are two exceptions: (1) Rings adjacent to the main ring of multi-ring basins are consistently spaced at a slightly, but significantly, larger interval, (2.1 ?? 0.3)0.5D; (2) The 88 rings of 44 protobasins (large peak-plus-inner-ring craters) are spaced at an entirely different interval (3.3 ?? 0.6)0.5D. The statistically constant and target-invariant spacing of so many rings suggests that this characteristic may constrain formational models of impact basins on the terrestrial planets. The key elements of such a constraint include: (1) ring positions may not have been located by the same process(es) that formed ring topography; (2) ring location and emplacement of ring topography need not be coeval; (3) ring location, but not necessarily the mode of ring emplacement, reflects one process that operated at the time of impact; and (4) the process yields similarly-disposed topographic features that are spatially discrete at 20.5D intervals, or some multiple, rather than continuous. These four elements suggest that some type of wave mechanism dominates the location, but not necessarily the formation, of basin rings. The waves may be standing, rather than travelling. The ring topography itself may be emplaced at impact by this and/or other mechanisms and may reflect additional, including post-impact, influences. ?? 1987 D. Reidel Publishing Company.