The collision-induced rototranslational hyper-Rayleigh spectra of gaseous H 2 – He mixture are computed and discussed in the binary regime. As the input data we use our ab initio computed H 2 – He collision-induced first dipole hyperpolarizability tensor Δ β ( R ) . Both the vector and the septor part of the H 2 – He hyper-Rayleigh spectra are evaluated at room temperature ( T = 295 K ) . The spectra are calculated assuming the full quantum computations based on the Schrödinger equation of the relative translational motion in the isotropic H 2 – He potential as well as using semiclassical methods.