One interpretation of the Magellan data suggests that the cratering record on Venus was erased by a global resurfacing event, or events, the latest ending about 500 m.y. ago. In this global-resurfacing model the resurfacing was followed by minor volcanism and tectonism that has been concentrated primarily in the equatorial highland regions characterized by extensive fracture belts and rifts. A thermal evolution model of Venus that can explain these observations is one in which a deformable lithosphere, capable of being incorporated in mantle circulations, provides an almost stress-free condition at the surface. Mantle convection with an almost stress-free boundary at the surface cools the interior more efficiently. Rapid cooling decreases the Rayleigh number of mantle convection below a transition value required for oscillatory convection, and the vigor of convection diminishes as the mantle changes to a quasi-steady circulation after about 500 m.y. ago. ¿ American Geophysical Union 1993