The effect of non-stoichiometry on the crystal structure and total conductivity of Ln 2+x Zr 2−x O 7−x/2 (Ln=Sm–Gd; x=0–0.286) was investigated. The intensity of the pyrochlore superlattice reflections from Ln 2+x Zr 2−x O 7−x/2 is shown to decrease with increasing Ln concentration. Within the homogeneity range of the pyrochlore phase of Ln 2+x Zr 2−x O 7−x/2 (Ln=Sm–Gd), the activation energy of high-temperature conduction in samples prepared by 1600 °C sintering of mechanically activated oxide mixtures (Ln 2 O 3 and ZrO 2 ) is ∼0.87–1.04 eV. The highest conductivity among the Ln 2+x Zr 2−x O 7−x/2 (Ln=Sm–Gd) materials is offered by stoichiometric Ln 2 Zr 2 O 7 samples with a pyrochlore structure, which contain 5–8.1% Ln Zr +Zr Ln anti-structure pairs, except for Gd 2 Zr 2 O 7 (∼22%). The crystal structure of Ln 2+x Hf 2−x O 7−x/2 (Ln=Sm–Gd) is investigated after sintering at 1000–1670 °C. The compounds Ln 2.096 Hf 1.904 O 6.9 (Ln=Eu, Gd) prepared by 1200 °C sintering of mechanically activated oxides (Ln 2 O 3 and HfO 2 ) undergo a fluorite-type to pyrochlore phase transition above 1200 °C. The conductivity of Gd 2 Hf 2 O 7 and Sm 2.096 Hf 1.904 O 6.952 sintered at 1600 °C seems to be ionic above 780 °C, with an activation energy of 0.77 and 0.82 eV, respectively. In this work, using mechanical activation of starting mixtures, the conductivity of the Ln 2+x Hf 2−x O 7−x/2 (Ln=Sm–Gd) hafnates was raised close to the level of Ln 2+x Zr 2−x O 7−x/2 (Ln=Sm–Gd). The hafnates synthesized by the procedure in question are similar in structural disorder to Ln 2+x Zr 2−x O 7−x/2 (Ln=Sm–Gd), and the disorder ensures high oxygen ion mobility and, accordingly, significant high-temperature conductivity.