Biciliate, gliding zooflagellate Cercozoa are globally the most abundant and genetically diverse predators in soil (glissomonads and cercomonads). We present the first detailed ultrastructural study of a phylogenetically well-characterized glissomonad, Allapsa vibrans. There are two ventral posterior centriolar roots as in Cercomonadida, but fewer other microtubular roots. Allapsa's centriolar roots and rhizoplast basically resemble those of the less well studied glissomonads Bodomorpha and Neoheteromita. The posterior centriole of Allapsa attaches laterally to the base of the anterior centriole and to the nucleus by striated fibrillar connectors and nests in a shallow cup-like ventrolateral depression; two broad fans of single microtubules line the cup's posterior and inner side. The anterior centriole has a dorsal two-microtubule root and probably also a singlet root. Its medium-length ciliary transition zones have a proximal hub-lattice and a prominent dense distal transverse plate/collar complex. Golgi bodies are anterior/paranuclear; isodiametric extrusomes are anterior mid-ventral. Tubulicristate mitochondria attach to the nucleus, as do prominent microbodies. We characterize the body plan of glissomonads, comparing it with other Sarcomonadea: their sister group (Pansomonadida) and the phylogenetically more distant Cercomonadida. We discuss glissomonad radiation into families Sandonidae, Proleptomonadidae, Dujardinidae, Bodomorphidae and Allapsidae, establishing Aurigamonadidae fam. n. for the amoeboflagellate pansomonad Aurigamonas.