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A detailed discussion of the optical properties of Al-rich Al1[?]xInxN alloy films is presented. The (0 0 0 1)-oriented layers with In contents between x = 0.143 and x = 0.242 were grown by metal-organic vapour phase epitaxy on thick GaN buffers. Sapphire or Si(1 1 1) served as the substrate. High-resolution x-ray diffraction revealed pseudomorphic growth of the nearly lattice-matched alloys; the data analysis yielded the composition as well as the in-plain strain. The complex dielectric function (DF) between 1 and 10 eV was determined from spectroscopic ellipsometry measurements. The sharp onset of the imaginary part of the DF defines the direct absorption edge, while clearly visible features in the high-photon energy range of the DF, attributed to critical points (CPs) of the band structure, indicate promising crystalline quality of the AlInN layers. It is demonstrated that the experimental data can be well reproduced by an analytical DF model. The extracted characteristic transition energies are used to determine the bowing parameters for all CPs of the band structure. In particular, strain and the high exciton binding energies for the Al-rich alloys are taken into account in order to assess the splitting between the valence band with \Gamma^{\rm v}_9 symmetry and the \Gamma^{\rm c}_7 conduction band at the centre of the Brillouin zone. Finally, the compositional dependence of the high-frequency dielectric constants is reported. [ABSTRACT FROM AUTHOR]