The solidification of a series of Bridgman-grown Al-Co-Cu alloys with compositions in the vicinity of the quasicrystal was studied by powder X-ray diffraction (XRD), differential thermal analysis (DTA), electron microprobe analysis, and optical microscopy. The phase equilibria and microstructure of solidified alloys are presented; the temperatures of the involved solidification reactions were determined. These experimental data were used to construct a solidification phase diagram as to understand the crystallization path. The decagonal (D) AlCoCu quasicrystals form incongruently, but they can be primarily solidified from off-stoichiometric melts.