Sr2MMoO6 (M = Mg, Mn) double perovskites have recently been proposed as anode materials in solid-oxide fuel cells (SOFC). The evolution of their crystal structures has been followed by “in situ” temperature-dependent neutron powder diffraction from 25 °C room temperature (RT) to 930 °C by heating in ultrahigh vacuum (PO2 ≈ 10-6 Torr) in order to simulate the reducing atmosphere corresponding to the working conditions of an anode in a SOFC. At RT, the samples are described as tetragonal (I4/m space group) and monoclinic (P21/n) for M = Mg, Mn, respectively. Sr2MgMoO6 undergoes a structural phase transition from tetragonal to cubic (Fm-3m) below 300 °C; Sr2MnMoO6 experiences two consecutive phase transitions to tetragonal (I4/m) and finally cubic (Fm-3m) at 600 °C and above. In the cubic phases, the absence of octahedral tilting accounts for a good overlap between the oxygen and transition-metal orbitals, resulting in a good electronic conductivity; a high mobility of the oxygen atoms is derived from the elevated displacement parameters, for instance 3.0 Å2 and 4.6 Å2 at 930 °C for M = Mg, Mn, respectively. Both factors contribute to the excellent performance described for these mixed ionic and electronic conductor oxides as anodes in single fuel cells. From dilatometric measurements, the thermal expansion coefficients (TEC) in the cubic region are 12.7 × 10-6 K-1 and 13.0 × 10-6 K-1 for M = Mg and Mn, respectively. These figures are comparable to those obtained from the mentioned structural analysis; moreover, the TECs for the cubic phases perfectly match those of the us- al electrolytes in a SOFC.