This article reports a study of the effect of anions on the optical Kerr effect (OKE) spectra of binary ionic liquid mixtures with one mixture comprising the 3-methyl-1-pentylimidazolium ([C5mim]+) cation and the anions PF6- and CF3CO2 - (TFA-), and another mixture comprising the [C 5mim]+ cation and the anions Br- and bis(trifluomethanesultbnyl)imide (NTf2-). The spectra were obtained by the use of optical heterodynedetected Raman-induced Kerr Effect Spectroscopy at 295 K. The OKE spectra of the mixtures are compared with the calculated mole-fraction weighted sum of the normalized OKE spectra of the neat liquids, The OKE spectra are nearly additive for [C5mim]Br/[C 5mim]|NTf2] mixtures, but nonadditive for [C 5mim][PF6]/ [C5mim][TFA] mixtures. In the case of the equimolar [C5mim][PF6]/[C5mim][TFA] mixture, the nonadditivity is such that the experimental OKE spectrum is narrower than the calculated OKE spectrum. The additivity or nonadditivity of OKE spectra for IL mixtures can be explained by assuming ionic liquids are nanostructurally organized into nonpolar regions and ionic networks. The ionic networks in mixtures will be characterized by "random co-networks" for anions that are nearly the same in size (PF6- and TFA-) and by "block co-networks" for anions that differ greatly in size (Br- and NTf2-).