The undercooling and nucleation of an Al65Cu20Fe15 alloy have been investigated with a 1.2-m-long drop tube. Melted droplets solidified either in vacuum or in helium. Various size samples in the forms of a globule, a fine fiber, and an irregular splat were collected at the bottom of the tube. X-ray phase identification results indicated that the CsCl-type cubic phase with a lattice parameter of 2.94 Å and Al-Cu-Fe icosahedral quasicrystalline phase coexist in most specimens. However, the amount of each phase differs in various size samples due to the different cooling rates and undercoolings. It can be concluded that deep undercooling is beneficial to the formation of the Al-Cu-Fe icosahedral phase. In addition, in some rapidly solidified fine fibers (<105 K/S), the Al-Cu-Fe ternary amorphous phase was also observed by high resolution transmission electron microscopy.