The viscosities of 23 ionic liquid (IL)-IL mixtures were measured at multiple temperatures and mole fractions. Many of the mixtures involved a dialkylimidazolium bis(trifluoromethylsulfonyl)imide ([Tf2N]) IL paired with a tetra-alkylphosphonium IL containing an aprotic heterocyclic anion (AHA). As a result, most of the mixtures contained both unlike anions and cations. The mixtures ranged from strongly positive deviations from the Arrhenius model (the mole fraction weighted logarithm of the viscosity), even having mixture viscosities greater than the viscosity of either pure IL, to negative deviations. Studies of complementary pairs ([C-1][A(1)] + [C-2][A(2)] and [C-2][A(1)] + [C-1][A(2)] mixtures) have identical viscosities at overall mole fractions of 0.50, clearly indicating that the anions and cations of the mixtures exchange freely. These mixtures cannot be well-represented by the Arrhenius model assuming a random distribution of the four possible cation/anion combinations (e.g., 0.25 mole fraction of each possibility at an overall IL mole fraction of 0.50). Rather, if one assumes preferential formation of some cation/anion pairs to match the experimental viscosity data at a 0.50 IL mole fraction, a much better representation of the data can be obtained. However, additional IL-IL interactions are needed to explain maxima in the experimental viscosity data. Excess molar volumes are very small for all of the systems measured.