Glenesteroceras, which is of questionable validity, is based on a single specimen from the Lower Ordovician of New York state, described by Rousseau Flower, 1957.
Glenestoceras is described as being a weakly annulate orthocone with a circular cross section and large central siphuncle with slightly divergent necks, thick connecting rings, and expanded segments. Description is based on an incomplete immature phragmocone with a 5mm cross section.