Raman spectra of the tetragonal structure of paratellurite TeO2 have been revisited avoiding anomalous polarization-selection-rules violations previously observed and due to optical activity. We present a complementary hyper-Raman scattering study of paratellurite. Wavenumber and symmetry assignments are given for all expected 21 Raman active optical branches, except one LO component (out of the eight expected TO–LO pairs) of the polar doublet E modes. Also, the four expected hyper-Raman active A2 (TO) modes have been observed. Moreover, we have observed a strong Kleinman-disallowed hyper-Rayleigh signal, which is tentatively assigned as a first evidence of hyper-Rayleigh optical activity. Copyright © 2013 John Wiley & Sons, Ltd.