We discuss the characteristic lineshape of the optical absorption of the novel "narrow-gap" InN in terms of the single-particle band structure and two-particle Coulomb interactions. More precisely, we explain the plateau in the imaginary part of the dielectric function, that follows the steep absorption onset, by the strong nonparabolicity of the conduction and light-hole bands near the zone center. The frequency range above 4.5 eV is dominated by higher optical interband transitions. The Coulomb attraction of optically excited electrons and holes leads to large redshifts of the spectral features and a strong coupling of the interband transitions. (c) 2005 Elsevier B.V. All rights reserved.