High-quality wurtzite In-rich In 1-x Ga x N (0 ≤ x ≤ 0.5) and In 1-y Al y N films (0 ≤ y ≤ 0.25) were grown on sapphire substrates by molecular-beam epitaxy. Optical absorption, photoluminescence and photomodulated reflectance measurements demonstrate that the fundamental bandgap for InN is only about 0.7 eV. The free electron effective mass is found to vary with free electron concentration, the consequence of a strongly non-parabolic conduction band caused by the k . p interaction with the valence bands across the narrow bandgap. The bandgap gradually increases with increasing Ga or Al content in In 1-x Ga x N or In 1-y Al y N alloys. The composition dependencies of the bandgaps are well described by bowing parameters of 1.4 eV for In 1-x Ga x N and 3.0 eV for In 1-y Al y N. The direct gaps of the group III-nitride alloy system cover a very broad spectral range from the near-infrared in InN to deep-ultraviolet in AlN. This offers unique opportunities for the use of these alloys in a wide range of optoelectronic and photovoltaic devices.