Transport numbers of oxygen ions, to2-, in methacomposites (1 - x)MeWO4 • xWO3, where Me = Sr and Ba and x = 0-0.55, are determined in the temperature interval 600 to 900°C by a method of the emf of an oxygen-air galvanic cell. It is demonstrated that the region of small contents of the additive (x ≤ 0.2) is predominantly characterized by oxygen-ion conduction (tO2 - = 1), which gives way to electronic conduction (t e = 1) at x > 0.35. It is confirmed once again that subeutectic compositions (1 - x)MeWO4 • xWO 3 where Me = Sr and Ba and x = 0-0.2 belong in the class of ion-conducting methacomposites. The threshold of percolation of electronic conduction (t e ≥ 0.5, tO2 - < 0.5) occurs at x t ≥ 0.3. Dependences of the transport numbers of the oxygen ions on the volume ratio between components in both composites resemble one another; specifically, the threshold composition contains nearly 20 vol % of WO3. The dramatic amplification (by 1-1.5 orders of magnitude) of the ionic conductivity in the methacomposites occurs at small contents of tungstic oxide (x ≤ 0.01). A chemical transport removal of excess tungstic oxide, which is segregated in the form of the surface compound MeW-s, from the surface of the MeWO4 grains destroys MeW-s, leading to a 10-15-fold drop of the ionic conductance. At x ≥ 0.05, the oxygen-ion conductance in the methacomposites is practically independent of their composition. A model for the formation and architecture of the methacomposites is qualitatively modified. The modified model takes into account doubled surface activity and mobility of the MeW-s phase with respect to MeWO4 and WO3.