We have conducted ab initio coupled-perturbed Hartree-Fock calculations on five different well-defined pi-bridges of varying chain lengths, N=CH-CH=N, CH=N-N=CH, CH=N-CH=N, CH=CH-CH=CH, and C=C-C=C end-capped with electron-donating amino groups, to examine the effect of the nature of the pi-bonding sequence on polarizabilities (alpha) and second hyperpolarizabilities (gamma). Second hyperpolarizabilities of the azine (N-CH=CH-N) conjugated system were found to be the largest, and those of CH=N-N=CH, the smallest for the monomeric model compounds of the same chain length. On the other hand, the gamma value varied in the order CH=CH-CH=CH > C=C-C=C > N-CH=CH-N > CH=N-CH=N > CH=N-N=CH for the dimeric model compounds, and the same order was observed for the trimeric model compounds. Polarizabilities and second hyperpolarizabilities were found to be associated with the nature of the pi-bonding sequence where the presence of the nitrogen atom in the conjugated backbone has a diminutive effect. Polarizabilities and second hyperpolarizabilities increase as the length of pi-electron delocalization increases and were found to be larger for polyene and polyyne systems than those of nitrogen-containing pi-conjugated backbones. Our ab initio calculations demonstrate that the nature of the pi-bonding sequence plays an important role in determining the magnitude of the second hyperpolarizability, which should be considered while designing novel organic molecules for third-order nonlinear optics.