Nd-14.2at%Al and Nd-20.0at%Ag eutectic alloys were containerlessly solidified in an 8m drop tube. The droplets were undercooled during the free fall in about 1s under reduced gravity condition in He atmosphere. The cooling rates at the solidification temperature were computed as a function of droplet size by making use of heat balance calculations. They were ranging between 40x10(3) and 0.8x10(3)Ks(-1) for droplets in size range of 100-900m diameters. Nusselt, Reynolds, and Prandtl numbers of the droplets were calculated. Microstructures of the alloys were analyzed and eutectic spacings were determined. Microhardnesses of the droplets with different sizes were measured to reveal a dependence on the cooling rates with which the droplets are solidified.