The second-order nonlinear optical coefficient of polyphosphazene oligomers of increasing size has been determined by using ab initio methods taking into account electron correlation and frequency dispersion effects. The calculated first hyperpolarizability per unit cell converges rapidly with respect to chain length. It attains an amplitude of about one-third of the one of classical push-pull systems. This amplitude can be strongly increased by replacing the nitrogen of the backbone by silicon. The effects of the side groups (H, CH3, F, Cl, Br, and OH) on the first hyperpolarizability have been investigated as well. The different results have been rationalized in terms of alternations of bond lengths and atomic charges. (C) 2004 American Institute of Physics.