Within Chordata, they are further classified as:

* Subphylum: Vertebrata (having a backbone)

* Class: Actinopterygii (ray-finned fishes)

* Order: Anguilliformes (eels)

It's important to note that "eel" is a common name used for many fish species with elongated bodies. There are actually several different orders of fish that have eel-like shapes, so they might not be closely related.