Modern parameter-free calculations using many-body approaches are actually the state-of-art in theory of condensed matter physics. The enormous effort dedicated to the ab initio description of the properties of materials is increasing exponentially based on advances of calculations taking the quasiparticle electronic structure, excitonic effects and local field effects into consideration. In this work, it was modeled properties of group-III nitrides and their alloys by means of ab initio methods. The ground-state (energetic, structural, elastic) and excited-state (energy bands, band parameters, dielectric functions) properties of the zincblend and the wurtzite polytypes of AlN, GaN, InN, and their “wurtzitic” alloys InxGa1-xN and InxAl1-xN are investigated within a cluster expansion approach using density functional theory together with the AM05 exchange-correlation functional. The total energies and the optimized atomic geometries of all 22 clusters classes of the cluster expansion for each compound are calculated. The computationally demanding calculation of the corresponding quasiparticle electronic structures is achieved for all cluster classes by means of a recently developed scheme to approximately solve the quasiparticle equation based on the HSE06 hybrid functional and the G0W0 approach. Using two different alloy statistics, strict-regular solution model and microscopic decomposition model, the configurational averages are calculated. The composition-dependent electronic structures of the alloys are discussed based on configurationally averaged properties of the ground and excited states. The influence of the alloy statistics on the composition dependencies and the corresponding bowing parameters of the band gaps is found to be significant and should, hence, lead to different signatures in the optical-absorption or -emission spectra of these Materials.