Ages determined for extraterrestrial samples by the Sm-Nd and Rb-Sr techniques are commonly assumed to record igneous crystallization events, because in solid silicates, Nd and Sr diffuse at exceedingly slow rates. However, we find that for coarse-grained igneous cumulate rocks from the Moon or from a large, thoroughly brecciated asteroid, this assumption may not be reliable. The Moon and at least one asteroid (the parent body of the eucrite, diogenite, and howardite meteorites) appear to have been largely molten at or about the time they formed. We have modeled global cooling of the Moon and large (R=40--250 Km) asteroids, starting at or near the solidus. A crucial factor in determining the prevailing interval (Ic) of cooling between igneous crystallization and isotopic closure, for any given depth in the crust, is the extent to which the body is insulated by a regolith/megaregolith layer of porous, fragmental impact debris. Given plausible assumptions regarding the thicknesses of such layers on the Moon and the eucrite parent asteroid (and regarding the radius of the eucrite asteroid), our results indicate that deep-crustal regions tend to remain above the Nd and Sr isotopic closure temperature for intervals that are long in comparison to the precision of modern Nd- and Sr-based age measurements, and in comparison to suggested chronologic scenarios of global differentiation. Ic intervals of as long as 100 m.y. may be common among available samples of primordial, deep-crustal cumulates from both bodies. Chronologies for the gross solidification of the Moon and the eucrite asteroid should allow for the possibility that any single age for a coarse-grained ''plutonic'' or cumulate-textured rock might be many tens of millions of years younger than the igneous crystallization age. ¿ American Geophysical Union 1991