Most studies of the anomalous electronic properties of the ${\mathrm{GaAs}}_{1\ensuremath{-}}{\mathrm{N}}_{x}$ alloy have focused on near-edge states, but x-ray spectroscopic experiments [V. N. Strocov et al., Phys. Status Solidi B 233, R1 (2002)] have now revealed anomalous properties deep inside the valence and conduction bands. Indeed, whereas N p character is found in GaN in the energy region near the valence-band maximum (VBM), when $\ensuremath{\sim}3%$ N is introduced into GaAs one finds that N p character exists about 2--3 eV below the VBM and as two narrow peaks just above the conduction-band minimum. First-principles calculations of the N p character in ${\mathrm{Ga}}_{32}{\mathrm{As}}_{31}\mathrm{N}$ and GaN show that the valence resonances are due the fact that the VBM of ${\mathrm{GaAs}}_{0.97}{\mathrm{N}}_{0.03}$ itself lies >2 eV above that of GaN. Thus, there is no need to involve an $\stackrel{\ensuremath{\rightarrow}}{\mathrm{N}}$As charge transfer to explain the data. This conclusion is further confirmed by our calculated valenc$\stackrel{\ensuremath{\rightarrow}}{\mathrm{e}}$conduction-band absorption spectra. We also show that the broken-symmetry core-hole calculations are necessary to explain, within the local density approximation (LDA), the energy of the N 1$s\ensuremath{\leftarrow}$valence-band transitions. As to the conduction-band peaks observed experimentally in the x-ray absorption, our LDA calculations do not reveal the sharp peaks seen in the measured spectra, leading to the possibility that the latter may not be related to substitutional N.