We have studied by high resolution ARPES the spectroscopic properties of the prototype charge density wave system (TaSe4)(2)I and of the closely related insulating compound (NbSe4)(3)I. We observe features dispersing with the lattice periodicity, including commensurate (in (NbSe4)(3)I) and incommensurate (in (TaSe4)(2)I) superlattice shadow bands. The spectral lineshape is anomalous in the normal metallic state, and the intensity is strongly suppressed near the Fermi surface. In the insulating CDW state the linear extrapolation of the leading edge rather than the peak position identifies the gap energy scale. (C) 2001 Elsevier Science B.V; All rights reserved.