A subphylum of echinoderms, made up of members having a flattened theca or body lacking pentameral symmetry. Homalozoans (also called carpoids) include four extinct classes of relatively uncommon primitive echinoderms ranging in age from the Early or Middle Cambrian to the Late Carboniferous. Homalozoans have a flattened, asymmetrical to bilaterally symmetrical theca often composed of a marginal frame of large elongate plates surrounding top and bottom central areas that had numerous smaller plates and were probably flexible.

One homalozoan class (Ctenocystoidea) has no attached appendages; two classes (Stylophora and Homostelea) have a single plated armlike or taillike appendage used for feeding or swimming; and one class (Homoiostelea) has two plated appendages at opposite ends of the theca, one used for feeding, the other for swimming. The mouth is located either on one edge of the theca or at the base of the armlike appendage, while the anal pyramid is usually at the opposite margin or corner of the theca. All homalozoans were apparently mobile, benthic, detritus or suspension feeders that had adopted a flatfish way of life. Because they have a typical echinoderm skeleton with single-crystal, multiporous, sutured, calcite plates, most researchers consider homalozoans to be true echinoderms. However, they seem only distantly related to other echinoderms that have well-developed pentameral symmetry. It has been argued that one class of homalozoans (stylophorans or calcichordates) is intermediate between echinoderms and several groups of chordates, thus making the class directly ancestral to the vertebrates. However, this proposal has not been widely accepted by other echinoderm or vertebrate paleontologists.