The temperature dependence of transport coefficients is theoretically examined for Al-Cu-Fe phases. We investigate the electronic conductivity, the thermoelectric power, the Hall coefficient, the thermalconductivity, and the Lorenz number. The spectral dependence of the resistivity is modeled by means of a wide and a narrow Lorentzian in accordance with results of ab initio calculations (LMTO-ASA, Kubo-Greenwood formula). This model extracts those properties from the ab initio results which are indispensables to consistently explain the transport coefficients mentioned above. Sub-diffusive transport is found in our ab initio results. The validities of both the Matthiessen rule and the Wiedemann-Franz law are analyzed. We generalize to the bulk quasicrystal where the narrow Lorentzian is found to become more pronounced than in the (1/1) approximant. © 2001 Elsevier Science B.V.