Bi-based, cubic pyrochlore phases have been of considerable interest over recent years as a result of their relatively high dielectric constants and low dielectric losses over a considerable frequency range around room temperature coupled with their relatively low sintering temperatures, enabling the possibility of co firing with e.g. Ag electrodes. This combination of properties makes such materials attractive candidates for multilayer capacitor and integrated device applications. The disordered structures and low temperature dielectric relaxation properties of two such misplaced-displacive cubic pyrochlores found in the Bi2O3-MIIO-Nb2O5 (M = Mg, Ni) systems, Bi1.667Mg0.70Nb1.52O7 (BMN) and Bi1.667Ni0.75Nb1.5O7 (BNN), have been determined. As for other recently reported Bi-pyrochlores, 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.