Regions of the lithosphere that undergo finite crustal extension but are subsequently allowed to thermally relax during a period of reduced tectonic activity may become regions of relative strength and therefore resist any further extension. The strengthening is a consequence of the temperature dependence of rock rheology and the local thinning of the crust bringing strong upper mantle olivine-rich rocks closer to the surface where they replace weaker lower crustal plagioclase-feldspar-amphibole bearing rocks. This concept, which I call postextensional mantle healing, is illustrated by the predictions of a numerical model. Although the model is based on the results of rock testing in the laboratory, the results do not depend on a particular choice of creep parameters for the lower crust. The Palaeozoic tectonic history of the Canning Basin (northwestern Australia) is characterized by a series of extensional episodes separated by periods of relative quiescence. In this paper, I suggest that postextensional mantle healing is responsible for the continuous shifting through time of tectonic activity between the several major depocenters. The tectonic development of the East African rift system follows a scenario similar to that of the Canning Basin: extensional structures inherited from two bursts of extension in the Early Mesozoic and Cretaceous have not been reactivated during the Tertiary rifting which is responsible for the present-day rift morphology. ¿ American Geophysical Union 1992