It is demonstrated that the NEXAFS spectra are a "fingerprint" of the symmetry and the composition of the binary nitrides GaN, AlN and InN, as well as of their ternary alloys In0.16Ga0.84N and AlyGa1 N-y. From the angular dependence of the N-K-edge NEXAFS spectra, the hexagonal symmetry of the under study compounds is deduced and the (p(x), p(y)) or p(z) character of the final state is identified. The energy position of the absorption edge (E-abs) of the binary compounds GaN, AlN and InN is found to red-shift linearly with the atomic number of the cation. The E-abs of the AlyGa1-yN alloys takes values in between those corresponding to the parent compounds AlN and GaN. Contrary to that, the E-abs of In0.16Ga0.84N is red-shifted relative to that of GaN and InN, probably due to ordering and/or phase separation phenomena. The EXAFS analysis results reveal that the first nearest-neighbour shell around the N atom, which consists of Ga atoms, is distorted in both GaN and AlxGa1-xN for x < 0.5.