Systems of classification are not hat racks, objectively presented to us by nature. They are dynamic theories developed to express particular views about the history of organisms. Evolution has produced a set of unique species ordered by differing degrees of genealogical relationship. Taxonomy, the search for this natural order, is the fundamental science of history. D.J. Gould (1987) This paper includes species investigated through many years starting with original material from museum collections. A great number of species in the genera Stephanodiscus Ehrenberg, Cyclostephanos Round and Cyclotella (Kützing) Brébisson, all in the family Stephanodiscaceae Makarova, are presented with holo-, lecto- and/or neotypes, type locality and information concerning nomenclature. A typus generis is given for each genus. Errors in the literature are pointed out and corrected. Species in the genus Stephanodiscus have the characteristic fasciculate morphology, they have fultoportulae, rimoportulae with their external tubular (long or short) extension and areolae internally with a domed cribrum both on the valve face and on the mantle. The typus generis is Stephanodiscus niagarae. Species in the genus Cyclostephanos have also the fasciculate structure, the fultoportulae, but their areolae have a domed cribrum only on the valve face and are flat on the mantle, their rimoportulae have only a simple external opening, often connected with a spine and a marginal alveolate structure, even though in some species weakly developed, which differentiate these species from those in the genus Stephanodiscus. The typus generis: Cyclostephanos novaezeelandiae. The genus Cyclotella includes species which have a smooth central area, none to several valve face fultoportulae, a simple alveolate marginal striation and the rimoportulae with an external round or slit-like opening, located on the mantle interrupting the ring of mantle fultoportulae. In some species complexes, however, the external opening of the rimoportula can be found on the valve face, near the valve face/mantle junction. The typus generis selected is C. distinguenda. Some other described species are transferred to the new genus Puncticulata Håkansson gen. nov. encompassing the species with an areolate central area consisting of areolae and valve face fultoportulae, in some species only fultoportulae in others only areolae, a complex alveolate striated marginal area, rimoportulae on the valve face at the end of a shortened interstriae. The typus generis: Puncticulata comta (Ehrenberg) Håkansson comb. nov.
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