The paper examines the phase transformations of composite powders based on Al63Cu25Fe12 that contain alloying elements (Ti, Cr, Si in the ratio AlCuFe : TiCrSi = 75 : 25). The powders are produced by mechanochemical synthesis and subsequent thermal treatment. Amorphous and crystalline powder mixtures form during synthesis; their annealing results in multiphase structures consisting of α, β1, and β2 phases. High-temperature x-ray diffraction has revealed an α-phase between 700 and 900°C. The new α-phase should be regarded as a 1/1 approximant of the nonequilibrium quasicrystalline phase. The maximum content of the approximant phase (68 wt.%) is observed after five-hour synthesis and subsequent annealing (T = 700°C, τ = 2 h) of pressed powders, microhardness of the particles reaching 8900 MPa.