Oxynitride phosphate glasses are a subfield of phosphate-based glasses, where part of the oxygen of the network has been replaced by nitrogen, in a process commonly called nitridation, of the phosphate melt. Because of this, the properties of the glasses are greatly enhanced, notably mechanical and chemical resistance, which has resulted in an important field with applications in glass-to-metal sealing or as electrolytes for solid-state batteries when processed as thin films. Whereas the properties of oxynitride phosphates have been thoroughly researched in view of their prospected applications, the elucidation of their structure remains uncomplete in some aspects, notably in the way that the network building groups are interconnected as well as from the point of view of the role of the modifiers onto the nitrided network structure. In the present work, 1D, 2D, REDOR, and INADEQUATE NMR experiments have been complemented with high-temperature NMR of lithium and sodium oxynitride phosphate glasses to study the structural arrangement of the building units and its evolution with temperature. The results have evidenced that the network organization adopted by the glasses distinctively depends on the nature of the modifier cation. However, the results exclude any significant phase separation or segregation of oxide and oxynitride regions, despite some clustering of nitride species may be occurring, mostly in the lithium-containing glasses.