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 $E_F$.