Boulders of late Cambrian age in conglomerates in Quebec and Newfoundland have been intensively collected and have yielded some 18 species which were referred by Ludvigsen et al. (1989) to either Theodenisia Clark, 1948, or to Peracheilus Ludvigsen, 1986. Most specimens are cranidia, rarely having the free cheek in place, and all 3 mm or less in length (sag.). Similar cranidia from strata in Vermont (Clark and Shaw, 1968), Maryland (Rasetti, 1959), Oklahoma (Stitt, 1971), Texas (Winston and Nicholls, 1967) and Alberta (Westrop, 1986) appear to be few and are in need of further study. No even partially complete exoskeleton has been found, so that isolated pygidia cannot confidently be referred to a particular species; no hypostome is known. The cranidium provides a limited basis on which to diagnose a genus, and while each of the species displays distinctive characters, it is difficult to discern one or more related groups among them. The present investigation of the holotypes of type species and material of four additional species shows how problematic is the use of current generic categories. I begin my account by pointing out differences in appearance between individual specimens. Such contrasts are greatest between the external surface of the exoskeleton and a mold of the inner, visceral surface, lesser differences resulting from exfoliation of the laminated outer layer of the exoskeleton (Fig. 1) at different levels. The holotype cranidium of Theodenisia, T. eminens (Clark, 1924) is a unique specimen, none other like it having been recovered, despite the intensive collecting. It has distinctive features, but because of its uniqueness I advocate that the name Theodenisia should only be used for this holotype (Fig. 2.1–2.3, 2.5, 2.6). The holotype and additional specimens of Peracheilus marcoui (Raymond, 1924), the type species of the genus Peracheilus, are described (Fig. 2.4, 2.7–2.15), together with four other species. These show (Figs. 3, 4) part of the range of morphology that exists, but there is little in common between them. For example, not all have S1 and S2 prominent, nor is the glabella widest anteriorly in all. Renewed intensive collecting, including from areas other than Quebec and Newfoundland, is needed in the hope of obtaining more nearly complete knowledge of the exoskeleton. Such knowledge may show whether or not a group, or groups, of related species can be recognized. As a temporary expedient I use Peracheilus? as a genus in which to include, with question, three of the species, and adopt the more recently proposed name Calculites Fortey, 1983 for the type species Acheilus microps Rasetti, 1944. In recording the material examined, I include isolated pygidia associated with cranidia in Rasetti's collection to show that they are present, but not to confirm that I consider they belong to the same species as the cranidium.