The structural arrangement of alkali-modified calcium aluminosilicate glasses has implications for important properties of these glasses in a wide range of industrial applications. The roles of sodium and potassium and their competition with calcium as network modifiers in peralkaline aluminosilicate glasses have been investigated by Al-22 and Si-29 MAS NMR spectroscopy. The Si-29 MAS NMR spectra are simulated using two models for distributing Al in the silicate glass network. One model assumes a hierarchical, quasi-heterogeneous aluminosilicate network, whereas the other is based on differences in relative lattice energies between Si-O-Si, Al-O Al, and Si-O-Al linkages. A systematic divergence between these simulations and the experimental Si-29 NMR spectra is observed as a function of the sodium content exceeding that required for stoichiometric charge-balancing of the negatively charged AlO4 tetrahedra. Similar correlations between simulations and experimental Si-29 NMR spectra cannot be made for the excess calcium content. Moreover, systematic variations in the Al-27 isotropic chemical shifts and the second-order quadrupole effect parameters, derived from the Al-27 MAS NMR spectra, are reported as a function of the SiO2 content. These observations strongly suggest that alkali ions preferentially charge balance AlO43- as compared to alkaline earth (calcium) ions. In contrast, calcium dominates over the alkali ions in the formation of nonbridging oxygens associated with the SiO4 tetrahedra.