Liquid Ag38.5Cu33.4Ge28.1 ternary eutectic alloy was undercooled by a great degree up to 175 K(0.22 TE). X-ray diffraction analysis reveals that its rapidly solidified microstructure is composed of (Ag) solid solution phase, (Ge) semiconducting phase and η(Cu3Ge) intermetallic compound phase. With the increase of undercooling, there occurs a transition from the cooperative growth of three eutectic phases to the preferential nucleation and growth of (Ge) phase. The (Ag) and η phases usually grow to form pseudobinary lamellar eutectic structure. When the undercooling exceeds 80 K, the structural morphology of primary (Ge) phase transfers from faceted blocks to branched dendrites. Some (Ge) dendrites look like flowers, which usually have 5—8 lobes. In addition, the number of lobes tends to increase as undercooling increases. The crystal surfaces of the flower-like (Ge) dendrite are {111} planes and the dendrite grows along the 〈100〉 preferred growth direction.