A number of lanthanide compounds LnX₂ (Ln=Sc, Y, La-Lu; X=S, Se, Te), LnY₂ (Y=P, As, Sb), and LnZ₂ (Z = Si, Ge) are known to crystallize with a structure derivable from only one aristotype, the ZrSSi type. This structure type contains square layers of silicon atoms (in general: square layers of the element of medium electronegativity). The structural deviations observed within the different compounds are usually small and principally affect this square layer. The space groups of the derivative structures under consideration are subgroups of that of the aristotype and the group-subgroup relations are outlined. Distortions of the square layers caused by electronic reasons can mostly be understood by applying simple electron counting rules. A number of compounds with chalcogen deficiency LnX(2-δ) is noted, too, in which the occurrence of vacancies in the square layers often leads to even larger superstructures.