Non-symmetric components of the transition hyperpolarizability are shown to be zero for molecules possessing cubic symmetry. Consequently, the vibrational hyper-Raman selection rules for such species are governed solely by a fully symmetric hyperpolarizability tensor and it is predicted that vibrational hyper-Raman scattering from octahedral molecules is very weak. (c) 2008 Elsevier B. V. All rights reserved.