Eutectic phase transition involves the competitive nucleation and coupled growth of two solid phases within one liquid phase. Phase selection especially under unequilibrium condition, may result in novel microstructures and thus affects the performances of eutectic alloys. Liquid Cu-10 wt.% Zr hypoeutectic, Cu-12.27 wt.% Zr eutectic and Cu-15 wt.% Zr hypereutectic alloys are rapidly solidified in the containerless process in a 3 m drop tube. During the experiments, the Cu-Zr alloys are heated by induction heating in an ultrahigh vacuum chamber and further overheated to 200 K above their liquidus temperatures for a few seconds. Then the liquid alloys are ejected out from the small orifice and dispersed into tiny droplets after adding the argon gas flow. The solidified samples are analyzed by Phenom Pro scanning electron microscope and HXD-2000 TMC/LCD microhardness instrument. The competitive nucleation and growth among (Cu) dendrite, Cu9Zr2 dendrite and (Cu+Cu9Zr2) eutectic phase become more and more intensive as droplet diameter decreases. The layer spacing in Cu-12.27 wt.% Zr eutectic alloy decreases when the undercooling increases. And the microstructural transition takes place from lamellar eutectic to anomalous eutectic. The microstructure of Cu-10 wt.% Zr hypoeutectic alloy is characterized by (Cu) dendrite and lamellar eutectic. Whereas the microstructure in Cu-15 wt.% Zr hypereutectic alloy consists of Cu9Zr2 dendrite and lamellar eutectic. For the Cu-10 wt.% Zr hypoeutectic alloy, with the decrease of droplet size, the primary (Cu) phase transforms from coarse dendrites into equiaxed grains, and the volume fraction of (Cu) dendrite becomes larger and larger. As for Cu-15 wt.% Zr hypereutectic alloy, the primary Cu9Zr2 intermetallic compound grows in a band manner, and with the decrease of droplet size and increase of cooling rate, the solidified microstructure transforms from band Cu9Zr2 dendrite plus lamellar eutectic into spherical cell structure. The three alloys reach maximal undercooling at 177 K, 156 K and 204 K, respectively. The Trivedi-Magnin-Kurz and Lipton-Kurz-Trivedi/Boetinger-Coriell-Trivedi models are used to analyze the dendritic and eutectic growth as a function of undercooling. Theoretical analysis indicates that both dendritic growth and eutectic growth are controlled by solute diffusion during liquid-solid phase transition. To further investigate the effects of cooling rate and undercooling on the mechanical properties of Cu-Zr eutectic alloys, the microhardness of each of different phases is determined. The microhardness of the primary (Cu) phase within Cu-10 wt.% Zr hypoeutectic alloy is strengthened with the increase of cooling rate. The microhardness of eutectic within the three alloys also increases with increasing the cooling rate and the initial alloy composition of the alloy.