Zr-substituted rare-earth molybdates Ho5.4Zr0.6MoO12.3 and unsubstituted La5.5MoO11.25 demonstrate appreciable mixed electron-proton conductivity in the 200-470 degrees C and 145-730 degrees C temperature range, respectively, under wet oxidizing and mild reducing conditions (air, Ar, Ar-5% H-2). Rhombohedral fluorite-like La5.5MoO11.25 showed the highest bulk conductivity of about 1x10(-5)S/cm at 400 degrees C in wet air and Ar. Its impedance spectra did not provide any evidence of the grain boundary contribution in wet atmosphere. Total conductivity of Ho5.4Zr0.6MoO12.3 fluorite is much lower and is 3x10(-7) S/cm at 400 degrees C in wet air. Besides, it should be noted that there is a grain-boundary contribution of Ho5.4Zr0.6MoO12.3 in wet air and Ar. Thermogravimetry data demonstrate that the fraction of strong structurally bound water and interstitial protons in La5.5MoO11.25 and Ho5.4Zr0.6MoO12.3 is similar to 0.02-0.03% in the range similar to 600-900 degrees C. The stability of Ho5.4Zr0.6MoO12.3 fluorite structure and fluorite-like rhombohedral La5.5MoO11.25 structure in extremely dry conditions under dynamic vacuum of 10(-6)-10(-7) mbar was investigated by in situ variable temperature neutron diffraction between 800 and 1400 degrees C to understand phase behaviour under mild reducing conditions in a wide temperature range. Rhombohedral fluorite-like La5.5MoO11.25 has been shown to be more resistant to reduction under vacuum below 1100 degrees C in heatingcooling cycles than is fluorite Ho5.4Zr0.6MoO12.3. Given the higher proton conductivity of Ln(5.5)MoO(11.25), this suggests that rhombohedral fluorite-like La6MoO12 - based molybdates are suitable for long-term use under mild reducing conditions and 600-800 degrees C.