Droplets of uncoated molten Si (0.4–0.8 mm diameter) have been undercooled 250 °C. Ge droplets of similar size have been undercooled 280 °C in a B2O3 flux. The observed nucleation onset temperatures of both Si and Ge droplets are at or below the predicted amorphous phase melting temperatures Ta1. The solidified structures were polycrystalline. The nucleation frequency I, calculated from the Si data (2×104/cm3 s at 240±20 °C undercooling), should be an upper limit of the homogeneous nucleation frequency of the crystal phase, since we did not establish that nucleation was homogeneous in our experiments. However, this limiting I for Si indicates that homogeneous nucleation of crystal would not become appreciable in laser pulsing experiments until the liquid Si is undercooled to well below Ta1.