The results of room-temperature spectroscopic ellipsometry study of single-grain face-centred icosahedral (fci) ZnMgY, ZnMgHo, and ZnMgEr quasicrystals in the spectral range of 0.1-6.5 eV are presented. Analysis of the optical conductivity spectra, carried out within a framework of the band structure hypothesis, reveals that an optical response of the fci-ZnMgRE quasicrystals is determined by a superposition of the intraband Drude-type contribution and that of the interband optical transitions across a pseudogap. The deduced parameters of the fci-ZnMgRE electron energy spectrum are close to their values determined previously from an analysis of the fci-ZnMgRE photoemission data. (C) 2010 Elsevier B.V. All rights reserved.