Anomalous structural evolution was induced in the equilibrium immiscible Co-Cu and Fe-Cu systems by 100 or 200 keV xenon ion irradiation at 77 K or room temperature. In the Co15Cu85 and Fe70Cu30 multilayered films, nanosized quasicrystals were formed in an amorphous matrix, through a two-step transition of crystal-to-amorphous-to-quasicrystal. The obtained quasicrystals are Co-Cu dodecagonal and Fe-Cu icosahedral phases with twelve-fold and five-fold rotational symmetries, respectively. The real compositions of the amorphous matrix were determined to be close to Co10Cu90 and Fe70Cu30, while those for quasicrystals are nearly Co20Cu80 and Fe50Cu50, respectively. Moreover, the same dodecagonal and icosahedral phases were also obtained in the specifically designed Co50Cu50 and Fe50Cu50 multilayered samples upon thermal annealing at 500°C and 850°C, respectively, confirming the existence of these new metastable states in the respective systems. Besides, our molecular dynamics study showed that either Co or Fe could be mixed with Cu at an atomic scale in forming some metastable alloy phases. The amorphous-to-quasicrystal transition was discussed in terms of the similarity in the atomic configuration between the quasicrystal and amorphous short-range orders.