Abstract: High resolution transmission electron microscopy studies on the lillianite group minerals from the Ivigtut cryolite deposit, Ivigtut, South Greenland revealed the existence of disordered intergrowths of lillianite/gustavite-like blocks (N − 4) and heyrovskyite-like (N = 7) structural blocks. One disorder sequence is examined in detail, which gave an average homologue number N = 4.92 corresponding to a composition of Pb_{3.92 2x}Bi_2·xAg_xS_6.92 with x ≈ 1.2. An Axial Next-Nearest Neighour Ising model was used to follow the fluctuations in the average homologue number N across the crystal. This yielded compositional fluctuations of the order of 70–170 Å over a 1800 Å region of the crystal, with a 202 Å lamella of ordered vikingite. Trends in the randomness of the gustavite-vikingite intergrowth were evaluated and the dominant slab sequence was found to be 4,4,4,7 and 4,4,7,7, suggesting that some longer period homologues may be stable. A number of defects were noted in which changes in slab widths were accommodated. The origin of these partially ordered/disordered lillianite homologues is discussed.