The structure and electronic properties of a series of substituted 1,3,4-triazolo-2-(N-phenyl) amidines have been explored in terms of their dipole moments and first hyperpolarisabilities using a semi-empirical sum-over-states and a time-dependent coupled Hartree-Fock approach. The presence of an electron-attracting group in the phenyl ring results in a sharp increase in the dipole moment which increases substantially to 20 D with the introduction of an electron-donating 4-(N,N-dimethylamino)phenyl group into the 5-position of the heterocyclic ring. Related triazoles containing electron attractors show unexpectedly large hyperpolarisabilities which exceed those found for many conventional donar-acceptor systems.