Introduction: Primitive Asaphida (possibly ancestral to some other asaphine groups), including families retaining the natant hypostomal condition, as well as other ptychoparioid features; protaspides resembling those of Ptychopariida (not "asaphoid"); not all families included may be monophyletic (i.e., Anomocaroidea as described here is likely a paraphyletic group).
Cephalon: preglabellar field wide; glabella typically parallel or gently tapering, with 3 or 4 pairs of furrows more or less of ptychoparioid type, palpebral lobes long, sickle-shaped; natant hypostome, median ventral suture; natant hypostome, some approaching conterminant.
Thorax: 10-13+ segments.
Pygidium: typically large, with broad, usually concave border, 2-10 axial rings.
Families: Anomocaridae, Pterocephalidae, Housiidae, Parabolinoididae, Dikelokephalinidae.
Representative Genera: Anomocare, Anomocarina, Glyphaspis, Housia, Inouyella, Mapania, Labiostria, Pterocephalia.

Introduction: As in typical Asaphida with the following additional defining characteristics:
Cephalon: bearing preoccipital glabellar tubercle; glabella elongate, subparallel to tapering forward, with defined occipital ring, curved, apostrophe-like pair of basal glabellar furrows isolated within glabella; hypostome conterminant (rarely impendent)
Thorax: typically 8 segments (6 to 9 in some Ceratopygidae)
Pygidium: typically rounded and without spines, but sometimes with a terminal spine or pair of spines (e.g., Thysanopyginae).
Families: Asaphidae, Ceratopygidae.
Representative Genera: Asaphus, Basilicus, Homotelus, Isotelus, Lannacus, Megalaspidella, Megalaspides, Neoasaphus, Niobella, Notopeltis, Ogygiocaris, Pseudogygites, Ptychopyge, Ptyocephalus.

Cephalon: Opisthoparian or marginal facial sutures, generally eyeless; glabella typically convex and pyriform, with 3 or fewer pairs of furrows, preoccipital glabellar tubercle sometimes present; usually long genal spines.
Thorax: usually 5 – 8 segments, but only 2-3 segments in progenetic Raphiophoridae, and up to 30 in Seleneceme (Alsataspididae), with long, narrow adaxial pleurae.
Pygidium: wide, typically triangular, narrow axis extending to posterior margin, border strongly declined, doublure very narrow.
Other: Asaphoid protaspis shows common ancestry; Raphiophorus is the only Trinucleioid (indeed the only representative of the order Asaphida) that continues beyond the Ordovician-Silurian boundary.
Families: Alsataspididae, Dionididae, Orometopidae, Raphiophoridae, Trinucleidae, 
Representative Genera: Ampyxina, Bergamia, Cnemidopyge, Cryptolithus, Dionide, Hapalopleura, Orometopus, Protolloydolithus, Raphiophorus, Seleneceme, Trinucleus.

Cephalon: with opisthoparian sutures, glabella typically truncate anteriorly and squat, 1-4 pairs of lateral furrows, 1p may be transglabellar; preglabellar field variable, sometimes absent, palpebral ridge typically well-defined, but separate from axial furrow (compare to sister group Remopleuroidea); genal spines typically present, of various length; median ventral suture rarely lost to secondary fusion; hypostome conterminant
Thorax: 8-12 segments, axis convex, pleurae typically wider than length of axis, typically with short, pointed ends (longer in Loganellidae).
Pygidium: micropygous to isopygous, variable shape, axis often extends majority of length, sometimes with post-axial ridge, posterior margin smooth or spined (1-5 pairs of marginal spines)
Families: Dikelokephalidae, Saukiidae, Ptychaspididae, Eurekiidae, Loganellidae.
Representative Genera: Dikelokephalus, Saukia, Eurekia, Loganellus.

Cephalon: with glabella expanding forward to anterior margin, effaced in later cyclopygids, may be fused with occipital ring; fixigenae reduced (except in primitive Taihungshaniidae), palpebral lobes lack distinct rims, and contact axial furrows at anterior ends, librigenae fused or separated by anterior median suture; hypostome relatively transverse, impendent, often with tripartite posterior margin; eye various sized (may be hypertrophied and convex (Cyclopyge), typically closely adjoined to glabella.
Thorax: 5-8(9?) segments.
Pygidium: medium to large (subisopygous in Nileidae), axis usually with 2-5 rings (but up to 20+ in advanced Taihungshaniidae), may be smooth, or with indistinct furrows.
Families: Cyclopygidae, Nileidae, Taishunghaniidae
Representative Genera: Cyclopyge, Nileus, Taihungshania.

Cephalon: with opisthoparian sutures, glabella bulges transversely anterior of occipital ring, with up to 3 pairs lateral furrows, eyes medium to very large, with narrow, wire-like socle, palpebral rims inflated, deep rim furrows, extending into axial furrows anteriorly; genal spines present.
Thorax: 9-12 segments, axis convex, pleural furrows diagonal, pleural tips typically point backward.
Pygidium: with spinose margin, spines flattened, united at bases, extending to axis; convex axis not extending to posterior margin, pleural field flat, typically furrowed and backward curving. Surface variously sculptured or granulose.
Families: Remopleurididae, Kainellidae, Opipeuteridae, Bohemillidae, Auritamiidae, Idahoiidae, Hungaiidae.
Representative Genera: Amphitryon, Apatokephalus, Auritamia, Bohemillia, Hungaia, Hypodicranotus, Idahoia, Kainella, Macropyge, Opipeuter, Pseudokainella, Remopleurides, Richardsonella, Robergia.