Experiments on reversed Fe-Mg exchange between olivine and Ti-rich magnetite [(Mg,Fe)2TiO4-(Mg,Fe)Fe2O4] show that the distribution coefficient for the exchange reaction 1/2Mg2TiO4 + 1/2Fe2SiO4 = 1/2Mg2SiO4 + 1/2Fe2TiO4 varies from approximately 2.4 to 1.8 In the range 800-1400 deg C and suggest that Fe-Mg titanium-based spinel [(Mg,Fe)TiO0.5O2] exhibits small positive deviations from ideal mixing (< / = 170 cal/mol) in this temperature range. Comparison of these results with those for aluminum-based spinels suggests that the Gibbs energy of the reciprocal reaction MgAl2O4 + 1/2Fe2TiO4 = FeAl2O4 + 1/2Mg2TiO4 is about 6.2 and 5.2 Kcal/gfw at 1400 and 800 deg C, respectively. A thermodynamic formulation for R3O4 FeO-MgO- Fe2O3-TiO2 spinels based on a second-degree Taylor expansion in terms of composition and cation-ordering variables is calibrated. It uses the above data in combination with homogeneous and heterogeneous equilibria for the Fe2TiO4-Fe3O4, Mg2TiO4-MgFe2O4, and Fe3O4-MgFe2O4 spinel binary joins. The resulting calculated activity-composition relations and cation-ordering schemes are in accord with available experimental data and petrological constraints. This model indicates that mg and Fe2+ are more strongly ordered between tetrahedral and octahedral sites in titanium-based spinels than in ferric-iron-based spinels (with MG2+ showing a tetrahedral preference relative to Fe2+ in both spinels) and predicts an approximately symmetrical miscibility gap for fd3m Mg2TiO4-MgFe2O4 spinels (TE approx. 400 Deg C).