Quasicrystals involving decagonal and icosahedral phases were formed, through two peritectoid reactions on low-temperature annealing, from a non-equilibrium cubic phase prepared by the ball milling of a mixture of equilibrium cubic phase and Al powders in Al—Cu—Co and Al—Cu—Fe systems. In both systems, the peritectoid reaction between residual Al and preliminary milled non-equilibrium cubic phase occurred first to form tetragonal Al₇Cu₂(Fe, Co) at 623 K. Subsequently, the same reaction between these tetragonal and the non-equilibrium phases occurred to form the quasicrystals at 773 K.