Previous descriptions of the crystallography and crystal chemistry of the sulphosalts cylindrite, incaite, franckeite and potosiite are reviewed and assessed. Our new electron diffraction and electron microscopy results are then described and interpreted; first for cylindrites and then for franckeites. Images with  and  zone axes are available for the first time (from appropriate sections produced by cutting, polishing and ion-beam thinning across the strong, natural (100) cleavage). These are crucial for analysing the nature of the two layer types in these minerals, and the way(s) in which they are stacked. Cylindrite is confirmed as having a 2-atom thick pseudo-tetragonal layer, while in the remaining species this layer is 4 atoms thick. It seems likely that in the latter these layers are SnS-type rather than PbS-type. Details of the corrugation of the layers are also revealed.