Linnaeus (1758) used the terms Craniata and Vertebrata interchangeably to include lampreys, jawed fishes, and terrestrial vertebrates (or tetrapods).
Hagfishes were classified as Vermes, possibly representing a transitional form between 'worms' and fishes.

Dumeril (1806) grouped hagfishes and lampreys in the taxon Cyclostomi, characterized by horny teeth borne on a tongue-like apparatus, a large notochord as adults, and pouch-shaped gills (Marspibranchii).
Cyclostomes were regarded as either degenerate cartilaginous fishes or primitive vertebrates.
Cope (1889) coined the name Agnatha ("jawless") for a group that included the cyclostomes and a number of fossil groups in which jaws could not be observed.
Vertebrates were subsequently divided into two major sister-groups: the Agnatha and the Gnathostomata (jawed vertebrates).
Stensiö (1927) suggested that the two groups of living agnathans (i.e. the cyclostomes) arose independently from different groups of fossil agnathans.

Løvtrup (1977) argued that lampreys are more closely related to gnathostomes based on a number of uniquely derived characters, including:
Arcualia (serially arranged paired cartilages above the notochord)
Extrinsic eyeball muscles
Radial muscles in the fins
A closely set atrium and ventricle of the heart
Nervous regulation of the heart by the vagus nerve
A typhlosole (a spirally coiled valve of the intestinal wall)
True lymphocytes
A differentiated anterior lobe of the pituitary gland (adenohypophysis)
Three inner ear maculae (patches of acceleration sensitive 'hair cells' used in balance) organized into two or three vertical semicircular canals
Neuromast organs (composed of vibration sensitive hair cells) in the laterosensory canals
An electroreceptive lateral line (with voltage sensitive hair cells)
Electrosensory lateral line nerves
A cerebellum, i.e. the multi-layered roof of the hindbrain with unique structure (characteristic neural architecture including direct inputs from the lateral line and large output Purkinje cells) and function (integrating sensory perception and coordinating motor control)
In other words, the cyclostome characteristics (e.g. horny teeth on a "tongue", gill pouches) are either instances of convergent evolution for feeding and gill ventilation in animals with an eel-like body shape, or represent primitive craniate characteristics subsequently lost or modified in gnathostomes.
On this basis Janvier (1978) proposed to use the names Vertebrata and Craniata as two distinct and nested taxa.
Linnaeus (1758) used the terms Craniata and Vertebrata interchangeably to include lampreys, jawed fishes, and terrestrial vertebrates (or tetrapods). Hagfishes were classified as Vermes, possibly representing a transitional form between 'worms' and fishes.
Dumeril (1806) grouped hagfishes and lampreys in the taxon Cyclostomi, characterized by horny teeth borne on a tongue-like apparatus, a large notochord as adults, and pouch-shaped gills (Marspibranchii). Cyclostomes were regarded as either degenerate cartilaginous fishes or primitive vertebrates. Cope (1889) coined the name Agnatha ("jawless") for a group that included the cyclostomes and a number of fossil groups in which jaws could not be observed. Vertebrates were subsequently divided into two major sister-groups: the Agnatha and the Gnathostomata (jawed vertebrates). Stensiö (1927) suggested that the two groups of living agnathans (i.e. the cyclostomes) arose independently from different groups of fossil agnathans.
Løvtrup (1977) argued that lampreys are more closely related to gnathostomes based on a number of uniquely derived characters, including:
Arcualia (serially arranged paired cartilages above the notochord)
Extrinsic eyeball muscles
Radial muscles in the fins
A closely set atrium and ventricle of the heart
Nervous regulation of the heart by the vagus nerve
A typhlosole (a spirally coiled valve of the intestinal wall)
True lymphocytes
A differentiated anterior lobe of the pituitary gland (adenohypophysis)
Three inner ear maculae (patches of acceleration sensitive 'hair cells' used in balance) organized into two or three vertical semicircular canals
Neuromast organs (composed of vibration sensitive hair cells) in the laterosensory canals
An electroreceptive lateral line (with voltage sensitive hair cells)
Electrosensory lateral line nerves
A cerebellum, i.e. the multi-layered roof of the hindbrain with unique structure (characteristic neural architecture including direct inputs from the lateral line and large output Purkinje cells) and function (integrating sensory perception and coordinating motor control)
In other words, the cyclostome characteristics (e.g. horny teeth on a "tongue", gill pouches) are either instances of convergent evolution for feeding and gill ventilation in animals with an eel-like body shape, or represent primitive craniate characteristics subsequently lost or modified in gnathostomes. On this basis Janvier (1978) proposed to use the names Vertebrata and Craniata as two distinct and nested taxa.
Craniate