Hexanchiformes is the order consisting of the most primitive types of sharks, and numbering just a handful of species.

Hexanchiform sharks have only one dorsal fin, either six or seven gill slits , and no nictitating membrane in the eyes.

The frilled shark Chlamydoselachus anguineus is very different from the cow sharks, and it has been proposed that it be moved to its own order Chlamydoselachiformes.