Cu-8 wt.%Al eutectic alloy was undercooled by up to 187 K (0.14 T_E) using a drop tube technique. The crystal growth and phase selection mechanisms were investigated during containerless rapid solidification. It is found that the microstructural morphology is characterized by lamellar eutectic growth at small undercoolings. However, if the liquid alloy is undercooled by more than 25 K, eutectic growth will be suppressed completely and the dendritic growth of (Cu) solid solution dominates its solidification process. When the undercooling exceeds 153 K, a microstructural transition from coarse dendrite to equiaxed dendrite takes place.