Aluminum-copper-silicon alloys lying in the monovariant through between the binary eutectic (Al)CuAl 2 and the ternary eutectic (Al)CuAl 2(Si) have been frozen unidirectionally over a range of rates from ca. 0.1 to 10 cm/hr and with imposed temperature gradients ranging from 150 to ca. 300°C/cm. The shapes of the growth fronts can be rationalized in terms of the ratio thermal-gradient/rate-of-solidification and the composition, as well as in binary alloys. The detailed morphologies of silicon are described for the different shapes of the solidification profiles, the six types of microstructures which appear in the AlSi alloys being formed, i.e., massive crystals, longitudinal fibers with or without lateral plates, complex-regular structures, complex-irregular structures, and polyhedral crystals. With regard to the CuAl 2 phase, the growth process is cooperative for planar and dendritic fronts. During cellular growth it appears as a semicontinuous matrix in which (Al) fibers are embedded. The conditions for existence of the observed microstructures are discussed with reference to the binary AlSi and AlCu systems.