Independent sucking/swallowing pharynges, as found in members of at least ten animal phyla, are pharynges that are opened by muscles that are not attached to the outer body wall. Their musculature is derived from either mesoderm or ectoderm, the latter taking the form of a myoepithelium. I review results of previous work on the morphology of independent sucking/swallowing pharynges among invertebrates and provide new information on the ultrastructure of the pharynx of the cyclostome bryozoan Crisia eburnea. The various morphologies of this type of pharynx have been used in some phylogenetic considerations, but only the myoepithelial sucking pharynx with a triradiate lumen was considered significant in analyses of relationships between phyla. However, I argue that this shape is the only one that makes an efficient suction pump, and this, together with different orientations of the myoepithelial pharyngeal pump and its phylogenetic distribution, indicates that the triradiate myoepithelial pharynx has evolved convergently in a number of lineages.