Full potential linear augmented plane wave calculations have been performed to study the electronic and optical properties of In-rich InxAl1−xN alloys in the hexagonal wurtzite structure. Compositions of x = 0.9375, 0.8125 and 0.6875 are considered which follow from replacing one, three and five In atoms by Al in the 32-atom supercell. The new form of exchange correlation, i.e. Engel–Vosko’s generalized gradient approximation within density functional theory, is employed. The calculations yield the band structure and total density of states as well as the imaginary part ε2(ω) of the ordinary and extraordinary dielectric function. The calculated dependence of the bandgap on the composition is in good agreement with recent experimental studies. A reversal of the valence band ordering is found between x = 0.8125 and 0.6875. The absorption features in the high-energy range of ε2(ω) are related to critical points of the band structure. The transition energies for these van Hove singularities are determined and their bowing parameters are discussed.