The microstructural evolution of Al72Ni12Co16 alloy at various undercoolings was investigated in this paper. A single-phase decagonal quasicrystal (D-phase) was obtained in the undercooled Al72Ni12Co16 alloy melts. Different microstructure morphologies of the D-phase were formed with increasing undercoolings. Based on Toner's model of the step growth of quasicrystals, the growth mechanisms of the D-phase under various undercoolings were discussed. The D-phases formed at various undercoolings in the undercooled melts show different microstructures owing to the change of preferential growth direction from the quasiperiodic to periodic direction. (C) 2003 Kluwer Academic Publishers.