The cationic framework structure of a whole new family of compounds with the general formula Bi-2(n (+) 2)MonO6(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, Bi10Mo3O24. 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-Bi2O3 fluorite-type framework, inside of which are distributed ribbons of {MoO4} tetrahedra which are infinite along b, one tetrahedron thick along c, and of variable widths of 3, 4, 5 or 6 {MoO4} tetrahedra along a depending on the family member (n value). These {MoO4} tetrahedra are isolated, i.e. without sharing any corner as in the [Bi12O14] columnar structural-type phase Bi[Bi12O14][MoO4](4)[VO4]. The structure of all these family members can be described as crystallographic shear derivatives from Aurivillius-type phases such as Bi2MoO6, the n = infinity end member. All these compounds are good oxygen-ion conductors.