The structure and second-order nonlinear optical properties of a series of helical pyridine-pyrimidine oligomers recently synthesized by Barboiu and Lehn have been investigated theoretically by combining molecular mechanics and quantum chemistry approaches. In the absence of substituents, the hyper-Rayleigh scattering response (betaHRS) and the projection of the first hyperpolarizability on the dipole moment (beta||) exhibit periodic variations with chain length, but these nonlinear optical responses remain small. The first hyperpolarizabilities can, however, be enhanced by adding substituents. The greatest enhancement is obtained by substituting the pyrimidine groups by donor groups. Moreover, regular distributions of the donor groups around the helices enable the design of supramolecular structures exhibiting dipolar, octupolar or Lambda-shaped nonlinear optical characters, evident from the values of the depolarization ratios in hyper-Rayleigh scattering. Therefore this theoretical investigation demonstrates the potential of helical structures for the organization of chromophores in such a way that they exhibit large and specific second-order nonlinear optical responses.