The disordered structures and low temperature dielectric relaxation properties of Bi1.667Mg0.70Nb1.52O7 (BMN) and Bi1.67Ni0.75Nb1.50O7 (BNN) misplaced-displacive cubic pyrochlores found in the Bi2O3–MIIO–Nb2O5 (M=Mg, Ni) systems are reported. As for other recently reported Bi-pyrochlores, the metal ion vacancies are found to be confined to the pyrochlore A site. The B2O6 octahedral sub-structure is found to be fully occupied and well-ordered. Considerable displacive disorder, however, is found associated with the O' A2 tetrahedral sub-structure in both cases. The A-site ions were displaced from Wyckoff position 16d (1/2, 1/2, 1/2) to 96 h (1/2, 1/2-éA, 1/2 + éA while the O' oxygen was shifted from position 8b (3/8, 3/8, 3/8) to Wyckoff position 32e (3/8 + éọ, 3/8 + éọ, 3/8 + éọ). The refined displacement magnitudes off the 16d and 8b sites for the A and O' sites were 0.408 Å/0.423 Å and 0.350 Å/0.369 Å for BMN/BNN, respectively. © 2007, Elsevier Ltd.