Chemical bonding in the cyclophosphazenes is studied from the point of view of the quantum theory of Atoms in Molecules (AIM). To that end, HF/6-31G** ab initio calculations are done on a collection of (NPX2)(3) derivatives for a wide set of -X substituents, and its electron density, rho((r) over right arrow, and pair density, rho ((2))((r) over right arrow (1)(r) over right arrow (2)), are obtained and analyzed. The (NP)3 ring geometry and bonding properties are basically maintained along the cyclotriphosphazenes. The PN distance and the bond critical point properties (electron density, Laplacian, etc.) lie between those of XNPX3, formally a double NP bond, and those of X2NPX4, formally a single NP bond. being much closer to the former than to the latter. The Laplacian of the electron density shows the PN bond to be highly polar, with a clear tendency of the P atoms to lose almost all of their five valence electrons, and a significant concentration of charge along the PN line, even though within the N basin. The charge on the ring N basins, P(N), remains almost invariant, -2.3 e, in all cyclotriphosphazenes, whereas the charge of the ring P basin, (2(P), varies from +2.9 to +4.0 e, depending on the electronegativity of the -X group. There is an inverse correlation between e(P) and the PN distance, the more electronegative -X groups shrinking the (NP)(3) ring more, even though only slightly. The partition of the pair densities indicates that some 0.63 electron pairs are shared between each P and its two N neighbors in the ring, this value being typical of a polar but largely ionic bonding situation. The three N atoms in the ring share 0.20 electron pairs per N-N group, a small but significant amount, even though no bond path line occurs linking them. The three-dimensional contour surfaces of del (2)rho clearly depict the molecular regions having a Lewis basic or acidic character. Ring N atoms behave as weak Lewis bases, whereas ring P atoms are preferred sites for a nucleophilic attack tending to remove, perhaps ionically, a -X group. These topological properties do explain the chemistry of cyclophosphazenes and agree well with the available experimental densities. The AIM analysis supports the main conclusions from the traditional Dewar's model of phosphazenes.