  Quasicrystals are assumed to be electronically stabilized by a Hume-Rothery
type mechanism. This explains most of the peculiar properties of quasicrystals.
The stabilization is investigated by electronic transport properties, as they
depend sensitively on the stabilizing interaction between the static structure
and the conduction electrons. Thin-film techniques provide samples which are
well suited for systematic investigations as a function of composition and
structural quality for Al-Cu-Fe and Al-Pd-Re i-phases. For a narrow range of
composition, large transport anomalies occur, reaching a
metal-insulator-transition in thin films of i-Al-Pd-Re. We discuss this in the
framework of a resonant scattering of the conduction electrons with the
quasicrystalline structure, leading to a reduced electronic mobility and
density of states (DOS) at the Fermi energy $E_F$.
