We present a comparative analysis of the order-disorder transitions in Ln(2)(M-2 (-) (x)Ln(x))O-7 (- delta) (Ln = Sm-Lu; M=Ti, Zr, Hf; x=0, 0.096) pyrochlore-like compounds and solid solutions existing in the Ln(2)O(3)-MO2 systems. In the range similar to 600-1200 degrees C, Ln(2)Ti(2)O(7) (Ln = Sm-Lu) and Ln(2)Zr(2)O(7) (Ln = Sm-Gd) undergo ordering transitions, F* -> PI -> P, which culminate in the formation of an ideal pyrochlore structure, P. existing between 1100 and 1300 degrees C. Above 1300 degrees C, Ln(2)Ti(2)O(7) (Ln = Gd-Lu), Ln(2)Zr(2)O(7) (Ln = Sm-Gd) and Ln(2)Hf(2)O(7) (Ln = Eu-Tb) exist as oxygen-ion-conducting phases, PII, disordered in both the oxygen and cation sublattices. Ionic conductivity data for Ln(2)(M(2-x)Ln(x))O-7 (-) (delta) (Ln = Sm-Lu; M = Ti, Zr, Hf; x=0, 0.096) synthesized at 1600-1670 degrees C indicate that the highest conductivity in these systems is typically offered by nominally stoichiometric (Ln:M = 1:1). disordered Ln(2)M(2)O(7) (Ln =Sm-Lu; M=Ti, Zr, Hf) pyrochlores containing anti-structure pairs (Ln'(M) + M'(Ln)) and oxygen vacancies (V ''(O)) on the 48f (O2) site. The highest conductivity of Yb2Ti2O7, in which the cations have the smallest radii among the lanthanides and Group IVa metals, seems to be due to the increased role of the geometric factor in the Ln(2)Ti(2)O(7) (Ln = Sm-Lu) pyrochlores with predominantly covalent metal-oxygen bonding M-O (Ti-O). The ion transport parameters in these materials are determined primarily by the relationship between the sizes of the mobile oxygen ions and conduction channels. (C) 2010 Elsevier B.V. All rights reserved.