The methods of field study and detailed morphological analysis using three-dimensional reconstructions and thin sections, developed by one Russian School, were applied to the abundant Precambrian and Cambrian stromatolites of the Adelaide Geosyncline. Although other schools either demand formal taxonomy for algal remains only, or use informal descriptive nomenclature of morphologies which they believe are determined entirely by environment, it is concluded that valid and consistent stromatolite form-taxa suggests biostratigraphic subdivision and intercontinental correlations. New forms Acaciella angepena. A. augusta, Baicalia burra and Boxomia melrosa, and an indeterminate form of Acaciella are described.