Two 6uorite-related modulated phases ( 1 and 1 ) occurring in the (1؊x) 1 2 Bi 2 O 3 ' xCaO, 0.20 < x < 0.29, system have been carefully investigated via electron di4raction and XRD. The satellite re6ections accompanying the strong 6uorite-type substructure Bragg re6ections were always found to be of G F ؎& 1 8 1 12242 2* F (F for 6uorite)-type and to be consistent with a lowering of the cubic m3m point group symmetry of 6uorite to rhombohedral 3 m point group symmetry in both cases. The type of rhombohedral symmetry, however, was found to be quite distinct. The 1 phase is shown to be a two-dimensional incommensurately modulated phase of R3 m( 00) 11 superspace symmetry while the 1 phase is shown to be a rhombohedral, commensurately modulated, superstructure phase. Ca/Bi metal ion ordering on the essentially ccp cation array is shown to be largely responsible for the observed satellite re6ections and an expression for this ordering is derived using a modulation wave approach to structural characterization.