We have succeeded for the first time in inducing epitaxial growth of metal films on quasiperiodic surfaces. Depositions of Au onto the tenfold surface of a decagonal Al-Ni-Co quasicrystal were originally attempted to create a quasicrystal of a single element as an epitaxial film. Although the desired film was not obtained on the clean surface, a multiply twinned AuAl2 crystalline layer with a (110)-oriented surface was formed with the aid of an In pre-deposition layer. The presence of pre-deposited In also worked as a surfactant for the case of Au-deposition onto the fivefold surface of an icosahedral Al-Pd-Mn quasicrystal and promoted the formation of an ordered film of Au-Al alloy. X-ray photoelectron diffraction images from this ordered film show that the alloy has an icosahedral structure as a long-range order, suggesting the formation of a quasicrystalline film.