Midplate seismicity associated with some former rift-zones is distributed diffusely near, but exterior to, the rift basins. This “basin-exterior” seismicity cannot be attributed to reactivation of major basin-border faults on which upper-crustal extension was concentrated at the time of rifting, because the border faults dip beneath the basins. The seismicity may nonetheless represent reactivation of minor faults that were active at the time of rifting but that were located outside of the principal zones of upper-crustal extension; the occurrence of basin-exterior seismicity in some present-day rift-zones supports the existence of such minor basin-exterior faults. Other hypotheses for seismicity exterior to former rift-basins are that the seismicity reflects lobes of high stress due to lithospheric-bending that is centered on the axis of the rift, that the seismicity is localized on the exteriors of rift-basins by basin-interiors that are less deformable in the current epoch than the basin exteriors, and that seismicity is localized on the basin-exteriors by the concentration of tectonic stress in the highly elastic basin-exterior upper-crust. All of the hypotheses considered here appeal to the presence of a rift zone to explain the characteristics of the basin-exterior seismicity, but the hypotheses differ in their implications for the seismic risk of former rift-zones and in their implications for the causes of midplate earthquakes in general.