The problem of non-linear scattering of unpolarized light is discussed. New relationships between the scattering intensities for unpolarized and polarized incident light are given. It is shown that the usual equation connecting the depolarization ratios for plane and unpolarized light does not hold for non-linear scattering processes such as hyper-Rayleigh and hyper-Raman scattering. A new relation between the two is given in terms of two additional intensity ratios. An expression for the depolarization ratio for unpolarized light is also given in terms of the hyperpolarizability tensor.