The modeling of transport properties of nonaqueous mixtures containing ionic liquids (ILs), such as viscosities, is still in its infancy. The aim of this work is to evaluate the capability of viscosity models that are based on Eyring's absolute rate theory and activity coefficient models to nonaqueous mixtures containing ILs. The Eyring-NRTL (nonrandom two-liquid) and Eyring-UNIQUAC (universal quasichemical activity coefficient) equations were extended to modeling ILs with cosolvent mixtures. The results were compared and discussed. For systems with large nonideality the Eyring-NRTL equation needs three adjustable parameters to give satisfactory results, while the two-parameter Eyring-UNIQUAC model could give completely satisfactory results for these systems. Less adjustable parameters will be beneficial when limited experimental data are available. So, the Eyring-UNIQUAC equation was further simplified to have only one adjustable parameter by suitable assumptions.