The second-order nonlinear optical properties of helicenes and phenylenes have been theoretically investigated at the time-dependent Hartree-Fock level using the Austin model 1 semiempirical Hamiltonian. Both the antisymmetric isotropic component of the first hyperpolarizability ((β) over bar) and its projection on the dipole moment (beta(parallel to)) have been determined for increasingly large helical systems as well as for their analogs substituted by donor/acceptor pairs. It is found that (i) in nonsubstituted helicenes and phenylenes, (β) over bar increases monotonically with the size of the system and slightly depends on the nature of the helix; (ii) the corresponding beta(parallel to) is mostly determined by the radial component of the first hyperpolarizability vector; (iii) in helicenes, beta(parallel to) is positive and presents quasiperiodic oscillations with the helix; (iv) in phenylenes, beta(parallel to) depends upon the size of the helix and it can be either positive or negative as a result of the differences in evolution with N of the radial components of the dipole moment and first hyperpolarizability. Substituting the helicenes and phenylenes by the prototypical NH2/NO2 donor/acceptor pair provides a diversity of effects on (β) over bar and beta(parallel to) that encompasses decrease, increase, and change in sign. (C) 2004 American Institute of Physics.