In the present study we report on the formation mechanism of some binary Al-TM and ternary Al-Cu-TM (TM = transition metal) quasicrystals. We have found that the formation mechanism of quasicrystalline phases in the binary Al-TM system takes place at extremely high solidification rates, is linked to the location of the transition metal in the periodic table, depends upon the atomic radius ratio of the constituents, is composition sensitive, and as a result is strongly affected by the effective atomic radius ratio (a eff ). Applying empirical criteria on the formation of ternary Al-Cu-TM quasicrystals we were able to calculate the composition range at which the formation tendency and stability of quasicrystalline phases is enhanced. The method presented can be viewed as an empirical criterion to find new and high quality quasicrystalline materials and to optimize the quasicrystalline material composition. Furthermore, it was observed that the stabilization mechanism of the quasicrystalline Al-Cu-(Fe, Co, Ru, Rh, Os, Ir) phases takes place when the atomic ratio (TM+Cu)/Al ranges from 0.46 to 0.69 and for a eff values between 4.10 and 7.30. At the same valence electron concentration, metastable icosahedral Al-Cu-(Cr, Mn) phases are formed at relatively smaller atomic ratios (TM+Cu)/Al and having higher a eff values in comparison to those of the stable D- and I-phases.