The optical properties and electronic structure of molecular-beam epitaxy grown InN and In-rich group III-nitride alloy films are studied. The band gap of InN is determined to be 0.7 eV by optical absorption, photoluminescence, and photo-modulated reflectance. The band gap exhibits weaker temperature and pressure dependencies than those of GaN and AIN. The narrow band gap leads to a strong k(.)p interaction, resulting in a non-parabolic conduction band, which is studied by the free electron concentration dependence of the electron effective mass. Highly n-type InN exhibits a large Burstein-Moss shift in the optical absorption edge; this effect may be responsible for the 1.9 eV band gap reported previously for some degenerately doped InN films. The band gap bowing parameters of the InGaN and InAlN alloy systems are determined. The band offset of InN with other group III-nitrides is presented and its effect on p-type doping is discussed. (C) 2004 Elsevier B.V. All rights reserved.