The cationic framework structure of a whole new family of compounds with the general formula Bi(2(n + 2))Mo(n)O(6(n + 1)) (n = 3, 4, 5 and 6) has been elucidated by transmission electron microscopy (TEM) methods. High-resolution transmission electron microscopy (HRTEM) has been used to postulate heavy-atom models based on the known structure of the n = 3 phase, Bi(10)Mo(3)O(24). These models were tested by HRTEM image simulation, electron diffraction and powder X-ray diffraction simulation methods which agreed with the experimental results. The four known phases of this family correspond to n = 3, 4, 5 and 6 members and all show fluorite superstructures. They consist of a common delta-Bi(2)O(3) fluorite-type framework, inside of which are distributed ribbons of {MoO(4)} tetrahedra which are infinite along b, one tetrahedron thick along c, and of variable widths of 3, 4, 5 or 6 {MoO(4)} tetrahedra along a depending on the family member (n value). These {MoO(4)} tetrahedra are isolated, i.e. without sharing any corner as in the [Bi(12)O(14)] columnar structural-type phase Bi[Bi(12)O(14)][MoO(4)](4)[VO(4)]. The structure of all these family members can be described as crystallographic shear derivatives from Aurivillius-type phases such as Bi(2)MoO(6), the n = infinity end member. All these compounds are good oxygen-ion conductors.