Isolated specimens of the appendage Anomalocaris canadensis have long been known; a single incomplete specimen of an animal having a pair of these appendages attached anteriorly is described. Seven dorsoventrally compressed, partly complete individuals of a similar animal that had a different pair of appendages (`F' of Briggs 1979) attached anteriorly are described, together with two obliquely compressed individuals that are thought to be conspecific. Surrounding the mouth of this latter species is a circlet of plates identical with the supposed medusoid coelenterate Peytoia nathorsti; this species is referred to Anomalocaris; Laggania is a junior synonym. As now understood, Anomalocaris was an animal that reached a length of 0.5 m, the elongate body having a head region bearing one pair of large, lateral eye lobes, each borne on a short stalk, the single pair of appendages attached at the ventral, anterior margin. The 13 segments of the appendage in A. canadensis bore paired spines on the inner side, short spines on the outer side, and there was a terminal, spinose 14th segment. The appendage in A. nathorsti consisted of 11 segments, the 2nd to 10th bearing on the inner side a graduated series of spinose blades, and spines on the lateral and outer sides, the terminal 11th segment ending in a group of spines. The circlet of plates surrounding the mouth was situated ventrally on the head region immediately behind the appendages; the plates bore teeth and the circlet constituted a jaw mechanism; additional groups of spines were present in the buccal cavity. Beneath the head region, behind the mouth, were three pairs of semicircular flaps, strongly overlapping: on the tapering trunk were 11 pairs of triangular lateral lobes, widest at the mid-length of the trunk, reduced progressively in size backward. These lobes were strongly overlapping in the same sense as the flaps on the head, and attached low on the sides. The trunk termination was short and blunt, without any projecting spine or lobe. Attached to the side of the body, above each flap and lateral lobe, was a multi-lamellar structure, apparently a gill. A thin cuticle covered the head region dorsally, and ventrally around the appendages and jaw circlet, behind this becoming a lateral strip that narrowed backward. It is suggested that a thin cuticle covered the trunk region dorsally and hung down beside the gills; this covering may have been continuous, but possibly was divided into tergites. Irregular patches of apatite, and some matrix, occur in the trace of the alimentary canal, which extended to the tip of the trunk. Mineralized patches occur in association with the gills, and as transverse strips, presumed traces of some internal organ or structure. The cuticle of the appendages and jaw circlet was presumably stout, hence these parts of the body were more resistant to decay and so were preserved in isolation. The thin cuticle of the lateral lobes shows rays which were presumably thicker and strengthening in function. We suggest that this animal, the largest known from Cambrian rocks, swam by using the series of closely spaced lateral lobes essentially as a lateral fin along which waves of motion were propagated. If the waves were moved in either the same, or opposite, sense on each side, considerable manoeuvrability would have resulted. The anterior pair of appendages, and jaw mechanism, would have made Anomalocaris a formidable predator, particularly on soft-bodied benthos including the abundant arthropods without a mineralized exoskeleton. No fragments of hard parts have been observed in the gut, but there is evidence that it may have inflicted wounds on trilobites. Anomalocaris was a metameric animal, and had one pair of jointed appendages and a unique circlet of jaw plates. We do not consider it an arthropod, but the representative of a hitherto unknown phylum. It is best known from A. nathorsti, the single specimen of A. canadensis having a different appendage but the rest of the body similar, probably including the jaw circlet. The evidence is insufficient to reach any conclusion on whether or not these two `species' may be sexual dimorphs of a single species. The single specimen of Amiella ornata is redescribed. It shows what may be lateral lobes like those of Anomalocaris, but other features unlike it. We conclude that this specimen is not an example of Sidneyia inexpectans, and is too incomplete for its relationship to be determined.