What classes of fish lack paired fins and jaws?

* Hagfishes are jawless, eel-shaped fish with a cartilaginous skull but no vertebral column. They have a single nostril, numerous slime glands, and a unique feeding mechanism that involves rasping prey with tooth-like structures on their tongue.

* Lampreys are also jawless, eel-like fish with a cartilaginous skeleton. They have a sucker-like mouth with sharp teeth that they use to attach to and feed on other fish.

These two groups are considered primitive fish, representing lineages that diverged early in vertebrate evolution. Their lack of paired fins and jaws reflects their adaptation to specific ecological niches and lifestyles.