Water line shifts were measured in solutions of 15 equimolal mixtures of two salts as a function of the total salt molality, mt. Several additivity rules were examined; the following predicts with reasonable accuracy the observed shifts for the alkali halides and (CH3)4NBr: δmixt = 1/2(a1 + a2)mt + 1/2(b1 + b2)mt2. Here a1, b1, etc., are parameters obtained from corresponding measurements on the pure salts, which take the form δ = ams + bms2 (ms, = salt molality). Two models of the origin of the quadratic term in this expression were investigated. In one model, due principally to Hindman, interaction of electrostrictive ion hydration with water structure-making or breaking produces a quadratic term. In the other, polarization of water molecules by more than one ion, a suggestion originally made by Schoolery and Alder and revived in the light of later measurements, is the cause. The shifts observed in salt mixtures, and various other results, were employed to test the two models. Information presently available does not allow a choice between the two. Shifts in salt mixtures involving (n-C4H9)4 NBr were not well accounted for by either model. The discrepancy may be related to strong R4N+- R4N+ interactions in these solutions.