The name ‘tobermorites’ includes a number of calcium silicate hydrate (C-S-H) phases differing in their hydration state and sub-cell symmetry. Based on their basal spacing, closely related to the degree of hydration, 14, 11 and 9 Å compounds have been described. In this paper a new nomenclature scheme for these mineral species is reported. The tobermorite supergroup is defined. It is formed by the tobermorite group and the unclassified minerals plombièrite, clinotobermorite and riversideite. Plombièrite (‘14 Å tobermorite’) is redefined as a crystalline mineral having chemical composition Ca5Si6O16(OH)2·7H2O. Its type locality is Crestmore, Riverside County, California, USA. The tobermorite group consists of species having a basal spacing of ~11 Å and an orthorhombic sub-cell symmetry. Its general formula is Ca4+x(AlySi6–y)O15+2x–y·5H2O. Its endmember compositions correspond to tobermorite Ca5Si6O17·5H2O (x = 1 and y = 0) and the new species kenotobermorite, Ca4Si6O15(OH)2·5H2O (x = 0 and y = 0). The type locality of kenotobermorite is the N'Chwaning II mine, Kalahari Manganese Field, South Africa. Within the tobermorite group, tobermorite and kenotobermorite form a complete solid solution. Al-rich samples do not warrant a new name, because Al can only achieve a maximum content of 1/6 of the tetrahedral sites (y = 1). Clinotobermorite, Ca5Si6O17·5H2O, is a dimorph of tobermorite having a monoclinic sub-cell symmetry. Finally, the compound with a ~9 Å basal spacing is known as riversideite. Its natural occurrence is not demonstrated unequivocally and its status should be considered as “questionable”. The chemical composition of its synthetic counterpart, obtained through partial dehydration of tobermorite, is Ca5Si6O16(OH)2. All these mineral species present an order-disorder character and several polytypes are known. This report has been approved by the International Mineralogical Association Commission on New Minerals, Nomenclature and Classification.