Ab initio and density functional theory calculations have been carried out on dipole moments (mu), polarizabilities (alpha), and second-order hyperpolarizabilities (gamma) of single chain beta-strand oligoglycines in the gas phase. Basis set and electron correlation effects have been investigated. The long-range corrected CAM-B3LYP and omega B97X-D functionals furnish satisfactory results in agreement with correlated ab initio computations. The dependence of gamma, alpha, and gamma values per unit cell on chain length has been explored, extrapolating the properties in the limit of the polymer. The increase of the response electronic properties with the number of glycine units has been rationalized through the two-state model involving the typical pi-pi* NV1 electronic transition of peptides. The effect of the secondary structure on the electric properties has been discussed. At variance from the dipole moments, the gamma values increase on going from the alpha-helices to the beta-strands, whereas the alpha values are little influenced by the conformation of the oligoglycines.