Cladistically speaking, nautiloids are a paraphyletic group united by shared primitive (basal) features not found in derived cephalopods. In other words, they are a evolutionary grade that is thought to have given rise to both ammonoids and coleoids. They are defined by the exclusion of both those descendent groups. Both ammonoids and coleoids probably descended from bactritids, which in turn arose from straight-shelled orthocerid nautiloids. 