Chemical arguments based on the S concentrations in the metallic magmas that formed magmatic iron meteorites and on the lack of pyroxene in pallasites suggest that core formation in asteroids was accompanied by >40% melting of the associated silicates. The existence of plagioclase-free residues from partial melting, such as lodranite meteorites, indicates that metal did not segregate from silicates when the amount of partial melting was only 15%. Thus, core formation in asteroids requires substantial melting of an asteroid. High interfacial energies between metallic melts and silicates require that metallic spherules sink through partially molten silicates to form cores in asteroids and planetesimals. The globule-sinking mechanism is not very efficient because silicate crystal-liquid mixtures have high yield strengths, making it difficult for the globules to sink. Calculations suggest that the melt fraction must reach >50% before globules can sink. Alternatively, porous flow of molten metal is possible when the amount of metal is high enough to form an interconnected network, about 50%; this can be achieved by high initial abundances of metal or by gradual removal of silicate melt, thereby enriching the residue in the metal-sulfide assemblage. This also requires removal of 50% silicate partial melt, though not necessarily all at once. Such high amounts of melting were not always attained in asteroids, so many asteroids probably consist of partially differentiated silicates and metallic masses that did not segregate to a core. S asteroids might represent such partially differentiated bodies. ¿ American Geophysical Union 1992